Learn Dutch: Laten we voor het protest verzamelen.

This happens because of the laten we ("let's") structure! When you use laten we to make a suggestion, the main action verb (verzamelen) stays in its full dictionary form (the infinitive) and goes to the very end of the sentence.

Doesn't voor also mean "before" or "in front of"?

Yes, voor is a very versatile preposition! Depending on the context, it can mean "for" (as in this sentence), "before" in time (voor het eten = before dinner), or "in front of" a place (voor het huis = in front of the house).

I thought verzamelen meant "to collect" things, like stamps or coins. Can it be used for people?

Yes! While verzamelen does mean "to collect" objects, it is also the standard verb for a group of people "gathering" or "assembling" in one location.

Could I use the emphasized pronoun and say Laten wij instead of Laten we?

You could, but it changes the tone. Laten we is the standard, natural way to say "let's". Using the emphatic wij (Laten wij...) sounds heavy, as if you are stressing "Let us gather (even if those other groups do not)."