Well, I don't see Aunt May (Extraordinay supporting character when she was written by JMS), MJ or Carlie so badly traumatized.
To be fair, they actually
should, but only because of Spidey related kidnappings and that kind of stuff that would leave anybody with at least a bad case of PTSD. Fortunately they are not portrayed like that. Maybe because in marvel universe,
your regular new yorker has already suffered all kind of weird stuff, including, just to name a few, hundreds of alien invasions, getting spider powers, or being possesed by symbiotes. Twice (Planet of symbiotes and one Mighty Avengers story)
Spidey stuff aside, Aunt May for example may have witnessed his husband's murder, but at least that is something anyone can have the misfortune of experiencing in real life (and as hard as it is, is something you can overcome without going mental)
With normal I mean unpowered people with normal lives (as normal as living in Marvel universe NY can be).
After all Peter is just some kid from Queens, not an asgardian god, an out of his time super-soldier or some rich super-inventor (Uh...
forget that last one I guess...)