Your bubba is not yet 5 months old. Of course he wakes up a lot.
He won't be in your bed when he is 7 but would it be the end of the world if he did come in for some cuddles? For many people jumping into their parent's bed in the morning is a treasured childhood memory.
If gentle disagreement isn't getting through I'd tell the nAsty mum that if she wants to be mean to her babies that's her choice and since you're not criticising it she should give you the same courtesy.
Sometimes when people criticise your parenting it's as much about being a bully as about what they really think about differant parenting styles.