We impose limitations on Free Speech for libel, slander, obscenity, pornography, sedition, hate speech, incitement, fighting words, classified information, copyright violation, trade secrets, non-disclosure agreements, right to privacy, right to be forgotten, public security, public order, public nuisance, and campaign finance reform. (This incomplete list scraped from Wikipedia). The means by which we decide these exceptions are by applying the principle of harm and the principle of offense, so named by John Stewart Mill. Specifically, we determine whether the speech actively causes, or is likely to cause, actual harm or whether it merely only has the capability to, but may not, cause harm.
On one side proponents will suggest that 'trigger warning' discussions are merely offensive to those who may possibly but will not necessarily be harmed - they are offensive but not harmful and this then is not enough to limit it as speech. Furthermore ample forewarning can be given to limit the exposure of someone sensitive to what is going to be spoken and a choice can be made in advance by someone who is sensitive to possible trigger warnings to participate.
On the other side, arguments can be made that (A.) exclusion from the debate based on the possible presence of trigger warnings legitimizes a paternalism because victims can not then show up to the debates (B.) the size of the class of potential victims and the scope of some discussions make it inevitable that harm will be done to someone or (C.) that the affects of open discussion on certain topics themselves have societal affects that cause harm as they institutionalize harmful norms (there are many examples from history).
There are topics and scenarios that exist on the boundary between the principle of harm and the principle of offense. Good arguments can fit these issues squarely into one or the other.