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Per the horribly worded description:

While you wear these boots, your walking speed becomes 30 feet, unless your walking speed is higher, and your speed isn't reduced if you are encumbered or wearing heavy armor.

But there are multiple ways in which a characters speed can be reduced beyond encumbrance. For instance, the Sentinel feat:

• When you hit a creature with an opportunity attack, the creature's speed becomes 0 for the rest of the turn.

Another example is being grappled:

• A grappled creature's speed becomes 0, and it can't benefit from any bonus to its speed.

I highlighted the word becomes in these descriptions because, in the English language, it would indicate a one-time change. So a boy BECOMES a man. A seed BECOMES a plant.

But the Boots also say, "While" -- A continuous duration. This puts the description at odds.

A character wearing the Boots has there walking speed "become" 30 feet unless encumbered or wearing heavy armor. They are hit by and NPC with the Sentinel feat so there speed "becomes" 0. Now what?

Does the character's speed re-become 30 feet allowing them to keep moving? Or are they forced to stand still?

I seem to recall there being another magic item that uses the a phrase similar to "cannot be reduced below" but so far my search has come up empty.

They likely only prevent reductions to your speed from encumbrance and heavy armor

First, it would be highly unusual if your speed constantly became 30 feet, this is not something which seems to come up elsewhere in the rules. Instead the Boots of Striding and Springing likely would have used wording similar to that used for effects such as the freedom of movement spell which states:

[...] Spells and other magical effects can neither reduce the target's speed nor cause the target to be paralyzed or restrained...

Additionally, if they wanted the Boots of Striding and Springing to prevent all reductions to your speed, there would be no reason to include the phrase:

[...] Your speed isn't reduced if you are encumbered or wearing heavy armor...

It is likely that what these boots do is they increase your base walking speed to 30 if it is not already higher. Any changes to your speed would simply apply to your new base. Effectively, they increase your speed by "30 - current_speed", though this wording is probably worse than the original.

Two examples:

If you normally had 20 speed, and something reduced your speed by 10 down to 10, putting on the Boots of Striding and Springing would increase your base speed to 30 and so your reduced speed would be 20.

If you normally had 20 speed, and were grappled (reducing your speed to 0). Putting on the Boots of Striding and Springing would increase your base speed to 30, but you would still have the grapple reducing your current speed to 0.