So what you are saying is the staff are treating a kid differently based on having a same-sex couple as parents?

If this is really happening, it is not normal and absolutely not acceptable. That's a serious accusation and one that will really disturb parents. You should raise this matter with the centre manager. And escalate this as far as necessary until it stops. Day care is supposed to be a safe place, not a place to introduce anxiety into a kid's world.

I don't know what channels and procedures are available to you, but please use them. There is a kid under your care that deserves someone in their corner.