Are you too jealous to allow your SO to hug or/and have a conversation with the opposite sex?

So, my husband gets super jealous if I were to hug a male friend(I’m not a hugger so it’s never really a problem)... I, on the other hand.. am not jealous about him having a conversation or a hug from a female as long as it’s not ya know flirting... but my SIL told me that I shouldn’t allow him that, and I should pull back the leash. He wouldn’t be happy if I were to do that to him so I should be more jealous. Idk about anyone else but does that not sound ridiculous? She goes on to tell me that she doesn’t even allow certain family friends (that are women) to hug her husband (in greeting).. and they are not allowed on his fb.... Please tell me I’m not crazy and that she is going way over board with all this. I mean harmless chit chat shouldn’t make me jealous.... right? I mean he’s MY husband.