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This all resolves if you realise that the term sought is: liberalism!

The linked Wiki page makes no mention of liberalism being a leftist thing.

liberalism (n.)

"liberal principles," especially the political principles of a liberal party, 1819, from liberal (adj.) in the political sense + -ism.

and

liberalism

• The quality of being liberal.


• (politics) Any political movement founded on the autonomy and personal freedom of the individual, progress and reform, and government by law with the consent of the governed. quotations ▼


• (economics) An economic ideology in favour of laissez faire and the free market (related to economic liberalism).

The term is not completely unambiguous. But the only confusion about the term concerning that a few people would consider this now to have anything to do with 'left' is that that 'reading' is a right-wing Americanism.

Don't use that word without explanation with Americans. And you'll be fine without complicated explanations in UK, Germany, France etc.

The word liberal has been so debased in America by right-wing demagogues that liberals have for at least two decades preferred to call themselves progressives.

–– Liberal? Are we talking about the same thing?, BBC

Exemplified in Wikipedia by making this necessary:

Modern liberalism in the United States

This article discusses liberalism as the term has been used in the United States since the 20th century. For the development of American liberalism, see Liberalism in the United States. For the origin and worldwide use of the term liberalism, see Liberalism.

JJJ gave a pretty good answer, but he eluded the part of your question where you also include "equality of opportunity", which itself is a non-trivial issue which much having been written about it. Equality of opportunity is probably impossible to fully address without an economic viewpoint... which you also seen to want to avoid taking a stance on.

On the other hand, if you want a centrist viewpoint on the latter issue of economics (rather than no viewpoint) then social liberalism and some synonyms thereof are the terms used to describe such a combination of centrist economic views with civil libertarianism:

Social liberalism, also known as left liberalism in Germany, modern liberalism in the United States and new liberalism in the United Kingdom, is a political ideology and a variety of liberalism that endorses a regulated market economy and the expansion of civil and political rights. [...]

A social liberal government is expected to address economic and social issues such as poverty, health care, education and the climate using government intervention whilst also emphasising the rights and autonomy of the individual.

So it depends how much of those issues like education, climate etc. you want to consider as being part of "equality of opportunity".

There's a much longer article on equality of opportunity on SEP: A bit of its conclusion section is worth quoting here

The slogan “equality of opportunity” commands wide allegiance among the members of contemporary societies. Under scrutiny, equality of opportunity divides into several different ideals, some of them being opposed rivals.

It's difficult not to subscribe to an economic viewpoint, as the economic system is deeply entwined with whether you are actually able to enjoy your individual rights. To some, a capitalist system is enabling, to others it is a barrier.

To arrive at a coherent philosophy, you need to also answer the questions

• do my individual liberties include trading away my individual liberties?


• do circumstances that limit my choices diminish my individual liberties?

A philosophy that emphasizes that individual liberties cannot be surrendered must have some form of remedy, should this ever happen, and that must involve help from other people if necessary.

(Interestingly, even Ayn Rand acknowledges this. There is a lengthy¹ passage in Atlas Shrugged where the inhabitants of Galt's Gulch mount a rescue mission for Hank Rearden, with everyone contributing to the best of their ability without charging each other for it.)

At the left and right ends of the spectrum, individual liberty requires that you also take responsibility to defend it. You can do so collectively or individually, with different trade-offs and failure modes. It is hard to envision a center position here².

¹ in other news, water is wet.

² that isn't reminiscent of Germany in the early 1930ies.

I was born and raised in the English language in the United States, my answer is based on that. Further, it is based on my 71 years on the planet, with an interest in political topics. The questioner correctly states that language can be abused, for instance that pro-Putin Russians use “liberal” as a negative (pejorative). To divorce liberal from leftist, my answer is you use the noun liberal with the adjective classical, hence: classical liberal.
Classical implies returning to an earlier time frame.
Libertarian implies more, sometimes unlimited freedom of choice, freedom of decision, as in using marijuana, ?-“because it doesn’t hurt others”-?

In order for it to be unambiguous, "Classical Liberalism" is probably what you're looking for. Merely "liberalism" will be quite context-dependent and definitely ambiguous. In the U.S. especially, 'liberalism' by itself now usually refers to the modern left, which is largely the opposite of classical liberalism, instead advocating for larger government and less economic freedom.

Wikipedia sums up Classical Liberalism as

a political ideology and a branch of liberalism which advocates civil liberties under the rule of law with an emphasis on economic freedom.

Is there an unambiguous term that describes a philosophy with a strong
focus on individual rights, equality of opportunity and freedoms, that
is also centrist on the socialism vs. capitalism spectrum?

This is key to your question. You describe a economics axis. Although many casual readers probably equate classical liberalism with capitalism, I'm not sure that's quite true. Classical liberalism believes in free markets. Capitalism means private ownership. They are arguably not the same; capitalism does not necessarily support free markets (crony capitalism, robber baron capitalism). So a classical liberal supports the role of the state in regulating the proper operation of free markets. A pure capitalist system tends to monopoly.

There is a lot of discussion about how much regulation is required for the proper functioning of a free market, which can be a broad debate amongst classical liberals. For instance, someone could say that structural inequalities may impede a class of certain individuals from fully participating in the market. This argument is rooted in classical liberalism. This is why it's such a broad, even stretchy term, I think.

So I would say that if you use the term "classical liberal", you are reasonably close.

Excellent question. Modern scholarship is contemptuous of left, right and center political spectrum; but it remains very important as the most widely used metric for describing modern and historical leaders and philosophies in use.

Your question presupposes that there is ambiguity in equating classic liberalism which, as you state, is better today classified as a moderate right leaning ideology(libertarianism); than with progressivism, the left, or modern liberalism(all synonyms). What you are missing is the understanding of what distinguishes left and right along with historical perspective.

The left is about new ideas, new solution when problems occur. Classic liberalism in the Age of Enlightenment when Jefferson, Paine, Beccaria, Baruch Spinoza, Diderot, Kant, Hume, Rousseau and Adam Smith first expressed them were new and thus liberal. Just as we say Stalin and Lenin were extreme examples of left ideology because they set out to create a new form of government.

The right or conservatism is about preserving the status quo. When conservatives face a problem they try previously used solutions or failing that reforming the existing system. We call the Roman senator Cato a conservative because at the end of the Roman Republic he dedicated himself to preserving the republic, the old system. He opposed the new, opposed empire. Alexander Hamilton is said to be the father of American conservatism for taking the opposite position. Hamilton favored recreating a monarchy in an age when monarchies were the norm. Hamilton and Cato both believed in the tried and true forms of government for there times but due to there periods supported opposite systems.

Hitler and Mussolini(fascism) are extreme examples of conservatism because in both Germany and Italy they were about recreating what had existed in the past. Hitler wanted to create the third Reich. Mussolini wanted to recreate the Roman Empire.

Each side has its advantages and disadvantages for moderate subscribers. Right leaning or conservatism tend to make safe well understood changes when confronting problems; however also by definition these solutions are compromises as there typically are reasons previous policies where changed. Conservatism really falls down when society faces systemic problems history has no answer for and reform is insufficient to address. ( ending slavery, labor laws after the dawn of the Industrial Age, trust busting, civil rights, woman’s suffrage ) Still conservative solutions are generally good safe solutions.

Left leaning or liberal solutions are inherently more dangerous with more unforeseen consequences. New ideas are inherently more risky than well understood previously tried solutions. Still without new ideas there is no progress. Most old ideas where at one time new ideas. Which brings us back along to libertarianism or classic liberalism.

Typically conservative ideology is most attractive after prolonged liberal rule; when society wants to introduce normalcy or just get things working again. Not coincidentally liberal ideology is most attractive and appealing after prolonged conservative rule. When society is struggling with systemic problems which history has no answer for.