How often do we actually see Reid refuse to give a handshake when a hand is offered? I can’t recall another instance. Hey, maybe there’s one. But he’s not rude, we’ve seen him give handshakes to an offered hand plenty of times. Usually he just doesn’t offer, so if the other person doesn’t either there’s no handshake.
The canon supports that he doesn’t like handshakes but will give them if it’s important to establish a relationship with the person. For example, in the 2nd and 3rd gif on the right of this gifset you can see Reid is the one to extend his hand to Mr Corbett. He might prefer not to shake hands but he knows it’s important sometimes. (Also, don’t discount the writers going OTT with the ‘oh noez Reid is socially awkward!’ stuff).
So, it comes down to the fact why is there such a big deal about Reid vocally refusing to shake Gordinski’s hand?
My interpretation: this is Reid making a not that subtle “dirty cop” jibe. If he’s not gonna shake his hand, then he’d just not shake; he makes sure to say something, and that something is about germs. Maybe the writers just intended for this to be a ‘lol Reid spews a fact’, but I interpreted it as a deliberate insult.
Gordinski is a racist cop who targeted young black boys for arrest and harassment, and used Carl Buford as his Token Black Resource in order to do it, enabling Burford’s abuse. In Profiler Profiled he states Buford had been helpful to his policing; that probably means funnelling ‘problem’ boys (read: kids that weren’t putting up with his abuse in the way he wanted) to be handled by Gordinski and co.
He didn’t even redeem himself in Profiler Profiled, let’s be honest: Morgan had to escape the police in order to prove that Buford was the unsub, Gordinski was so focused on Morgan as a suspect. Like literally so focused on persecuting Morgan that he decided that 13 yr old Morgan killed that first dead boy that was found, disregarding the age set out by Gideon’s profile on a loophole that the age might be different than the profile given.
I don’t think Reid has forgotten what kind of man Gordinski is; a racist cop who harassed his friend as a child and made it impossible for him to seek help from the police when he was being abused. A dirty cop who he doesn’t want to physically touch or give respect to beyond what is functionally necessary to get the job done.