Hey Anon! And yep, from the moment a demon who shape-shifted into idk how many animals…

can have intercourse with humans

then Shinigamis who originally are humans should be able to as well. 🙂

As for the “but they’re dead” part, well yeah, but we don’t know exactly what their condition is (I’ll elaborate below) and furthermore, they have primary needs like sleeping and eating so why not other needs? 

It’s kinda illustrated by Grell having the hots for several guys so far or even Ronald with most women actually, so to me it seems Shinigamis can feel attraction towards humans, which means they can surely be aroused and seek physical intimacy as a result.

Being able to have sex =/= being able to have kids: that’s a different debate. 

Just in case you were asking with this in mind though, I want to precise that  personally I think it’s possible for Shinigamis to have kids (so for example, I believe that the UT = Cedric theory is a possibility) because the Shinigamis aren’t exactly “dead”, the way final death is meant to be in Kuroshitsuji.

A human being is defined by two parts: their cinematic record and their soul. When they die, the CR is stopped by Shinigamis and to remain in the body, while the soul is collected. That’s what it means to be dead in Kuroshitsuji.

Now, if you look at UT’s bizarre dolls that are basically undead: they have no soul (because it was collected when they died and UT can’t make one from scratch), but they have edited cinematic records which is what makes the corpse mistakenly think it’s still alive. 

As for Shinigamis, well that’s the thing: we know they killed themselves so they should be dead…

but it seems they still have their soul and an unstopped cinematic record (otherwise how could they still move, think and feel?), in spite of their peculiar eyes or their ability to teleport, amongst other supernatural things. 

Furthermore…

…clearly they can actually die for real again if they’re hit by a death scythe (a death scythe being used to stop a CR and collect the soul, which is why I think they still have both). 

Becoming a Shinigami is a punishment to humans who took their own life so maybe they’re not exactly “dead”. Maybe, similarly to how some humans can be “judged worthy to keep on living” by Shinigamis when they’re fated to die, Shinigamis are special cases of “(not really) dead people”. 

All that to say, if they’re not exactly dead, then why wouldn’t they be able to have kids? Don’t get me wrong, we know they have superiors who are most likely scaring the shit out of them and as such, rules to follow were mentioned like…

…because Shinigamis are supposed to be “neutral between Gods and humans”, meaning they’re not supposed to be meddling with humans and have kids with them (or with other Shinigamis I suppose). 

As far as UT is concerned though, clearly he fails at being a Shinigami, so him having kids (the UT = Cedric theory) would just be one more broken rule to add to his record. No biggie. 

TL;DR yes, Shinigamis can most likely have sex with humans and with other Shinigamis. 

And from the moment they’re scared to die if stabbed by a death scythe, they might not be exactly dead the way other humans who don’t kill themselves are dead, so they might be able to have kids with humans or other Shinigamis, even though it is very probably 100% forbidden (since they are forbidden from meddling with life, death and humans).

I hope it answers your question Anon, sorry for the length! As with everything, it’s just my opinion, no one has to agree! 

Have a nice day. :))