Privately or corporately owned forums can legally protect their domain from dialog that is deemed harmful to public good or simply to prevent legal liability. They can go further and even impose a value of civility. Its akin to your workplace rules that enable employers to impose standards of appearance and conduct up to a point. The internet has changed from simple information exchange to a largely anonymous ideological megaphone. As the internet has grown people shifted from discussion forums to echo chambers. The crowd has moved to the corners and lob insults and lies at each other. Media outlets are struggling with the reality that they are complicit if they make no effort to remove disinformation that threatens public health, endorses violence, seeks to subvert fair elections or promote racist hate (whoever is saying it), When jihadists post disinformation about Western nations or post slick recruitment videos we all concur they should be removed. When bots spread unfounded harmful slander to subvert national security, when dangerous stunts like poison Tide pod challenge videos are posted, etc. media platforms rightly respond with removal of the posting or closing accounts.
So to answer your question, : Should Social Media Silence Conservative Views?
It depends upon the view being spread by the conservative. If the conservative is discussing the relative importance of free trade as opposed to tariffs or is encouraging celibacy before marriage, or is arguing for the private ownership of guns, it is very unlikely to be silenced. Unfortunately what is sometimes presented as a "conservative view" is actually just plain old political lies, inciting violence or racism being spread by a conservative. I have seen the similar approach by posters identifying as liberal while retweeting or sharing disinformation. They have been flagged as well. One account I know was closed for repeat offenses.