"An open mind is like a fortress with its gates left unguarded".
Thing of it is, there ARE safe and unsafe ideas (or, more commonly, safe and unsafe presentation of ideas). And it's critical thinking skills that render you capable of safely handling unsafe ideas / presentations.
You're right that the introspection is valuable, and that encountering "unsafe" ideas should lead to it; so I'm going to suggest: it's a person's attitude towards introspection that realizes the risk posed by an idea.
> who want to silence debate
IMO these people are just very badly communicating the idea "stop talking about other people's lives, and have those people speak instead" (plus layers of baggage and trauma). Halle Berry's recent controversy over a trans role is a good example of this; people talked about how she should't play the role (and some other issues), what they meant was "someone who lived this story should tell this story".
> people are strong/wise enough
Yes. Do you support massively more funding for education? Or do you see something else as a means to fight for this?