As a girl who has OCD stemming from cleanliness/germophobia/fear of contamination (I am currently in therapy) you are absolutely NTA. Like you said, there’s no visible stains and you obviously wash them, so there shouldn’t be a problem. I am very much seeing symptoms of serious OCD or something else similar.
I feel like society has kinda warped the popular perception of OCD so I’ll explain it a bit more to give context to what your BF might be feeling: OCD is an anxiety disorder. We perform our compulsions because we have anxiety that if we don’t, then X, no matter how unrealistic or silly X may seem (F.e. I used to never sit on my couch unless I’d showered and the couch was clean, because I didn’t want to get myself/my PJs “dirty” before getting in bed/going to sleep and I didn’t want to get the couch “dirty” either. If someone who I deemed “unclean” sat where I normally sat, then I would later use a cleaning spray on it before I next sat there)
I shower every day. The fact that your BF showers twice a day is kinda concerning. He very likely has compulsive rituals and routines when doing so , what with his cleaning himself 3 times. I speak from experience, as I was almost the exact same before I started therapy. My showers used to be anywhere from 1-1.5 hours
In my personal opinion I really don’t think he meant to make you feel gross, but rather he speaking out of extreme paranoia. I know I’ve definitely said stuff to people I never would’ve said if not for extreme OCD related anxiety in that moment. I used to constantly be “monitoring” the people around me including my family, to see if anything they did would trigger it, and if they did, I’d either point it out to them or sit in an anxious silence. I used to remember/keep track of when stuff got dirty and still get anxiety over it even if it happened months ago.
Maybe try having another talk with him later and trying to find out what’s really wrong. It’s definitely something deeper than him just thinking it’s disgusting. I really think he needs some therapy.