I think what is troubling, if anything, to the 'old people' (and probably not just those), is that when arguments such as this starts getting validity beyond be

I think what is troubling, if anything, to the 'old people' (and probably not just those), is that when arguments such as this starts getting validity beyond being appeals to civility - i.e. when someone is effectively able to stop discussion of a subject because they claim to be 'harmed' by it - it completely changes the context of the discussion and IMO, hinders constructive discourse. So, if safe spaces are to be a 'thing', then we have to be very clear that they must have a very well-defined limit, beyond which regular discourse can continue.