Nope, not at all.
As two adults with parental responsibility, each has a right to pursue their own relationships without any controlling behaviour from the other. If there are concerns about safety, there are routes to take that don't involve demanding to meet and basically judge this other person's choice of partner. Either via Family Court, or if more immediate concerns, social services/school.
In a more balanced co-parenting partnership, without the one-upmanship about who is better for the child, you might find that the other parent introduces their partner as a personal choice, but I can tell you that when there is bitterness and judgement, I wouldn't feel comfortable doing anything of the sort and the other parent would just have to deal with it.
Two people's issues with each other due to relationship breakdown has absolutely nothing to do with their parenting, if there are concerns about parenting, there is clear actions to take, if action has been taken and the child remains in the other person's custody, then obviously the child is being cared for adequately? No parent has a perfect history or perfect judgement.
All this I say coming from learning this personally through experience (and making my own mistakes), and currently trying to get custody of my own child due to concerns. I cannot judge anything about my ex other than whether I think he is a risk to our child's health, safety and well being, and then my responsibility was not to return them to his care until I'd ascertained via social services and CAFCASS they were at no immediate risk, and then follow the legal process to look at where they'd be better off living.
I'll have a moan about him, but having gone through the whole process of Court, CAFCASS, parenting course etc, I have come to see that our opinions of each other are not relevant, we need to put them aside and focus on what is, and that's the child. You can't change what you have no control over, and it's better to find common ground between yourselves and support each other (no matter how imperfect and frustrating the other parent is) because anything else only damages the child's experience.