The Constitution uses the following in regard to protest in the first amendment
Congress shall make no law ... abridging ... the right of the people peaceably to assemble, and to petition the Government for a redress of grievances.
It uses this same "right of the people" in the second amendment
... the right of the people to keep and bear Arms, shall not be infringed.
In both cases, the right is restricted to "the people." Note in the first amendment, only the final bit about protests is restricted to "the people" the rest is generally protected whether it is "the people" or not.
Note in Heller and elsewhere it was determined "the people" are those who belong to the political class (which is a bit vague, refer to next sentence, but not same as voting class). Generally this is not those on non-immigrant visas or illegal aliens (though circuits are split on this). If you don't have the right to bear arms, clearly you are not "the people" since people by definition have the right to bear arms, which means you wouldn't have the right of "the people" to protest either, no? So it appears since they are not people, they don't have the right to assemble in protest, though they may have other first amendment rights since it's protest specifically that was narrowed to "the people" rather than many of the other parts of the first amendment which are worded without that narrowing.
For instance, speech without assembly isn't narrowed to just "the people." Perhaps this was done intentionally since allowing non-people to stage protests was seen as less desirable than merely allowing them to otherwise speak freely.
Note: Personally I do think non-immigrants are people, but trying to apply the same "people" two different ways with the exact same wording makes no sense. If they can't bear arms they necessarily are not "the people" and thus are not afforded the right to "assemble, and to petition the Government for a redress of grievances."