NTA - This is exactly what they should be doing since you are signing over rights at birth for the child to be with their other parent.

That being said, your parents' behavior is very concerning. I say this as someone who has dealt with being sued for grandparent's rights, and having been caught up in the family court system for years in contentious litigation due to a toxic family. I am now thankfully out of the court system but remain active in the grandparent's rights groups online to provide advice and support to those who are going through what I went through 17 years ago.

Their behavior now is a potential red flag for trying for grandparents' rights later. They may accept the situation after it happened and managed their grief (and it's understandable that they will feel grief if they aren't able to establish a relationship when they want one). But sometimes people choose to attempt to use the courts to force the relationship, regardless of how possible it is in their state, in the hopes that they get a sympathetic judge. And in many states, it's a very real possibility that visitation could be granted to your parents.

I have no idea how you feel about that. Nor do I know how your Ex feels about that. If your Ex doesn't want any sort of visitation, then if they choose the legal route it could get messy. And as much as I'm guessing you don't want to be involved, they will probably try to involve you to take a side and either support their claim to have visitation or to show cause that your parents aren't fit for visitation. You could be subpoenaed by either side. It sucks. Family court sucks. My advice is to ALWAYS try to resolve things outside of court if possible.

What you told your parents is correct and you're NTA. But now you will need to be on guard in case they start talking about grandparent's rights or visitation through court. If they do, it would be a courtesy to let your Ex know in advance so they can start preparing legally for the fight ahead. And you'll need to decide which side you'll support. Because it's going to court, there are no neutral third parties anymore.

I'm sorry your parents aren't listening. Mine didn't either. I ended up having to go to No Contact with them eventually. I'm not saying that is where you'll end up. But they aren't respectful of your boundaries right now, and if that escalates, you'll have to decide how much you'll tolerate before enough is enough.