Pro-trans people often assume that gender dysphoria is just the natural result of having a brain of one sex in a body of another sex. Anti-trans people often assume that cisgender people are not attached to their sex at all. If we are to believe self-reports, though, there seems to be a wide range of attachment to one’s sex.
A reasonably consistent finding is that about 50% say that they care at least somewhat about staying their sex, whereas maybe 35% don’t care much either way, and 15% would rather be the opposite sex. This seems to be a continuum rather than discrete. The cis people who care enough that they’d try to medically transition back if they somehow magically had turned into the opposite sex are a minority, at least if you go by people’s introspection, but they are easily detectable in surveys.
Attachment to one’s sex is strongly negatively associated with sexually fantasizing about being the opposite sex. This may be an example of autogynephilia/autoandrophilia, but there are certain arguments against this (in particular, this’d imply that A*P is incredibly common).
From what I can tell, there are plenty of anecdotes of people who for whatever reason unrelated to gender dysphoria had to transition. Many of these people seem fine with it. Some were distressed initially, but eventually started liking it.
All of this does not seem like what we’d expect under Magical Innate Gender Identity.