There are two ways these agencies get involved. Probably more, but two that are relevant right now.
One is: Is this person fit to be a parent? This is where abuse and neglect come in.
The other is: Which parent is more suitable as the primary caregiver? This is where abuse and neglect are not all that counts. The big question they ask is: what's best for the child? Financial and emotional stability are major factors here.
I'm all for activism, but a custody battle is not the best venue to fight for equality. Your life = your consequences = your choice. The activists can pipe down.
If it were me, I would outright lie to the investigator. I would deny being polyamorous and claim that my ex is just saying that to tarnish my reputation. I would tell them that when we were married, my husband was dating his current girlfriend, and that if anyone is polyamorous, it's him. But mostly, I would focus on the abuse and how that affected your kids.
The point is, if you know the investigator is biased, then it's unlikely you're going to be the magic light that changes their mind and makes them realize that polyamory can be a perfectly healthy and happy environment in which to raise kids.
Do I like this from the perspective of polyamory getting equal rights? Of course not. But is it worth losing your kids to be "right?" Well, that's up to you.
As an aside, it's not just about sex in front of your kids. If you're dating people who are coming in and out of your kids' lives, and your kids are forming attachments to people and then those people are leaving, it can have deleterious effects on the kids' ability to form healthy relationships in the future. It can trigger anxiety about meeting new people over fear that those people will just vanish one day. Kids don't always understand grown-up relationships, and it's even possible the kids could believe it's their fault. Some of this is "worst case scenario" but it's important to be aware of possible consequences of dating different people when you're a parent.