There would be limitations because although we have the right to assemble and protest which is said in the 1st Amendment, it says you have to be peacefully assembled. If they are trashing the parks trashing the park and are making a mess of the park then it would be a great risk to public health. They can protest and assemble without trashing the park and they can peacefully assemble in the parks without risking the whole public's health. Therefore it would be reasonable for them to do some sort of punishment like community service or something like that.
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I hope this helps and it makes sense i assume this wasn't what you whole essay was about and if it was then hopefully this is enough or it at least gives you an idea.