It’s your house, so you can say no. I would be most concerned that he shares the room with a younger sibling who cannot be exposed to sexual activity, whether your son & a boyfriend or girlfriend are above the legal age of consent or not.
It’s great you have some good dialogue with your son (being open with his sexuality) so I think he’ll understand the legal issue surrounding a partner staying over with him with his brother in the room.
I allowed my kids at 16 to have friends sleepover, but only after we had open discussions about keeping safe (both with pregnancy and STIs) consent & how to access free condoms, sexual health checks & other contraception.
With my son being 4 years older than my daughter, we did talk about appropriate behaviour in the home outside of the bedroom. He also asked his sister for consent & respected her wishes if she wasn’t happy with the situation & didn’t want it to occur. Sometimes she wasn’t happy & her brother respected that.
My reasoning has always been, they’ll do it anyway & anywhere, so we offered a safe space where if they were going to experiment with sex, they knew there was open communication to talk about anything they needed to, without judgement. And that included the consent of their partners & us talking honestly to their parents too.
I had a violent, extremely strict upbringing so went a little boy mad at 16 (I think just to feel affection & loved) having liaisons here, there & everywhere. And discussions about contraception & safe sex were banned in the house (I was thrown against a stone fireplace by my father when I asked my Mum for advice one day), so we’ve always worked towards open, honest conversations with our kids. I had my son as a teenager & I didn’t want my children to go through that struggle.
It’s all about communication (I think I say that here a lot 😂).