I have always asked for mutual sti tests when considering moving from condoms to none.
It's only really been two people that I've done that with. The others, wr just used condoms throughout the relationship.
(One guy did rub against me before putting a condom on once, and passed on an std - either it was that incident or I got it from him even while using condoms; which is possible with that std. He was, I discovered, extremely promiscuous, so unfortunately it was not entirely unexpected).
On the subject of the std tests - both partners were reluctant. Both had not been asked to do it before.
The first claimed his ex (and only partner without condoms) was scrupulous about her sexual health and got tested regularly. I insisted on the tests; he went reluctantly (there was much moaning about dreading swabs inside his urethra etc. If that's what's it called on men too). He was given a booklet on clamydia and a course of antibiotics as a result of the tests.
(I ended up taking antibiotics as a precaution too).
The second guy, as above, claimed he'd never been asked even once to do tests, and said he'd had sex without condoms with all previous partners. (About 4/5, since he had been widowed young).
He reluctantly did them, and apparently there was nothing found; but I never saw his results, and discovered during the course of the relationship that he was a fairly glib, repetitive liar. So it's not impossible he didn't tell me if anything was found. I trusted him at the time but in retrospect, don't.
Anyway ... I'm waffling to try to say that I ask for them, but my experience of two men (one about 28 when I asked, the other about 45) was that they didn't do them, hadn't been asked previously and thought it was unnecessary and almost outlandish.
If I'd not persisted with the first guy, I could have had a case of clamydia without clear symptoms affecting my sexual health and fertility.