LONG POST AHEAD: but need your opinions!

Okay so a little background on this story: my boyfriend and I have been together for 3 years and are expecting our first child in March. We are over the moon excited! My boyfriend was adopted when he was a baby. His bio mom and dad were meth addicts and NOT good people. Later in life, he reconnected with both his bio mom and dad. His bio mom is still an addict and we both have cut all ties with her (she will not be apart of our child’s life). His bio dad is not on hard drugs but he is a functioning alcoholic and I am not the biggest fan of him, as he is a horrible influence on my boyfriend, but my bf wants so bad for him to be in his life as he’s never had any male influence growing up. His adopted mom and dad split up when he was first adopted, so he lived with his adopted mom and sister his whole life growing up. His adopted mom is a good person (she is super caring, sweet, sober, and had his best interest most of his life). BUT she (and his sister) are the grossest, laziest people I think I’ve ever met. I wouldn’t even consider her a hoarder, she just is a slob. Her house is NEVER picked up. There is always clothes EVERYWHERE (kitchen, bathroom, hallways, bedroom floors), there is always a horrible stench in the kitchen from mold growing in her dishes from not doing them, they have 3 dogs, 1 cat, and 2 rabbits and all of them roam and shit and piss where they please (on the carpet, beds, couch, literally anywhere and everywhere) AND THEY JUST LEAVE IT! It is horrific. On top of that, his moms ex boyfriend, her ex bf’s current gf, and his current gf’s 30 year old daughter all live in their 3 bedroom house, and they are all slobs too!!!! When we recently told them (his adopted mom and sister) we were pregnant they were overjoyed and so excited for us. They mentioned how they want to babysit on Friday’s cause she doesn’t work. Later, when we left I told my bf they are not babysitting and our kid is NEVER allowed in their house. I don’t even like going there do to the mold and infections I can get from dog and cat pee/poop, let alone our baby. He completely agrees, but is really sad because neither of his mom’s will be apart of our kids life. I also told him I don’t even know if I want them holding our baby when it’s so tiny. I don’t know when the last time they did laundry or if the dog/cat/rabbits have decided to go to the bathroom on the clothes they wear. And I don’t want my baby, who won’t be able to lift their head, leaning and breathing in the poop/pee shirt. Am I overreacting and being too overprotective because it’s my first baby? I feel bad and I dont want to have to tell them they can’t hold the baby, but I’m not willing to risk my baby getting sick from that. I’m just so torn.

And: If I don’t let her hold the baby, how do I tell her why she can’t?