Unless the content is called out for inaccuracy, bigotry, etc the user may not even be aware of the issue they create. Like if someone retweets a claim they believe but it is flagged as misleading and fact checked that might be the first time their views were checked and they might recognize their beliefs are wrong and rethink things. But they often won't and I think that is as much part of the problem. Trump won't rethink his position because a tweet was fact checked, he will attack the fact checker and supporters will do the same thanks to his example. There is no self reflection or awareness when called out and the poster becomes defensive, refusing to accept their comment as fake news or bigotry.
If conservatives feel they are being silenced but cannot recognize that the views 'censored' are often bigoted, racist, or simply unpopular or abhorrent outside their bubble, then what do you to? If you call out blatant racism you are less likely to find the user recognize their racism, apologize, and not use such language again and more likely to be called a snowflake and have that behavior turned up a notch. If the original comment is then downvoted by the community or removed by mods then it will enforce that persons view that they are being attacked. This is incredibly common on Reddit where users often include a 'bring on the downvotes' type edit after stating something intolerant or clearly false.
The solution is not to allow these views and opinions to sit unchecked but to recognize a modern civil society must be intolerant of intolerance and moderate appropriately. Downvote and report racist comments. Apply fact checking to statements, even those you believe or feel to be true as that is a sign of bias. If the user doubles down, move on as there is no value in arguing with someone putting their feelings and beliefs/bias above facts and reality. Perhaps when society or their online community turns their back on their comments they will finally have the time to reflect on why and recognize their behavior was unwarranted and unwanted.