There is a worse side effect that comes from conservatives feeling that they have been silenced, as people feel like they have less and less say in a political process they are more and more likely to start employing means outside of it. The real risk here is that if more and more outlets for conservative voices are silenced, whether for good cause or not, this will reinforce the narrative that many of them have that they are the defenders of the truth and right and there is a vast conspiracy operating to seize their guns, deprive them of their rights, and whatever else they can imagine. As that happens there becomes more and more moral justification and greater and greater need there is seen to employ violence in end of their goals.
Ultimately the more and more "dangerous" opinions and people who share those opinions are silenced the more and more dangerous they become in reality.
EDIT:
The nature of this comment is intended to be observational not advocational.