Some activities do, that’s the point of the first amendment (or, alternatively, a law becomes void when it is demonstrated that it does restrict freedom of speech). Other activities do not because the first amendment doesn’t apply to them. It doesn’t make murder or arson legal. I could imagine trespassing laws running afoul of the first amendment in some cases, particularly if they were applied government land, or to land where private companies have been given licence to extract natural resources.
Ideally the analysis should be done objectively. The law treats all people equally (in theory) so it can’t matter who is doing it. It can matter what is being done, though, and often people make some pretty specious analogies between different forms of protest. Blocking entrance to a government building is not the same as blocking entrance to an energy plant is not the same as blocking entrance of a medical clinic.
In the first case removal might be in order but presumably people should tread carefully about arrests. In the second I’d say it depends a lot on the specific circumstance and why the protest is happening and whether the building is public or private (though I think the public has a certain interest in power plants even if they are technically run by private entities). In the third case I’d say that one person’s right to protest can’t interfere with another person’s right to medical treatment. That’s not because I favour one policy over the other, it’s because it’s obviously different to obstruct one thing than another and it has different impacts and conflicts (or doesn’t conflict) with other constitutional rights. Like how in my first example, I imagined there was such a thing as a generic government building - really there isn’t. If it’s an office building where corporate types work then I’d have a very different attitude than if it was a courthouse doing small claims - the former is disrupting non-necessary work, the latter interfering with people’s rights.
I can’t imagine they ever would, which is what makes a law against protesting in that way an awful law that targets protest groups in an unacceptable way. Tampering with power plants is almost certainly going to be pretty damn criminal to begin with. Adding on additional penalties because it was part of a protest is a flagrant violation of the first amendment. Their first amendment right is not going to protect them from charges related to dangerous vandalism of public infrastructure, but it should obviously protect them from a law that specifically targets the fact of the protest, and it should definitely protect other members of a group that they claim to be part of from being fined by association.
In the last election in Canada one party suggested they would start a “barbaric cultural practices” tip line to report things like honor killings. If there was an honor killing next door, I’d call the police to report murder, not a special racist tip line to go after people for being Muslim while murdering. When something is already a crime, we don’t need a law against protesting while doing it. Either the first amendment overrides the law against the thing or it doesn’t, but it definitely overrides the extra-punishment-because-it-was-a-protest law, which is what this law appears to be.