If a dude walked away from his child, now 10 years later wants to all of a sudden pop back up after the child has two loving Moms in his life, should he just be allowed to come in now with doing this?

Yes and no. As the father he still has rights. If he goes to court he will probably be allowed visitation. So it might be better to bite the bullet and come to some agreement.

The courts allowed my biological father to pop in and out of my life from the time I was 6 till I was well... still to this day and I'm 20! Give him a chance it might not last long, but then again he could have just grown a brain and realized he needed to step up.

First men and women change, he may have settled down and now regret not being part of the child's life.

Next as the bio father he has rights, so he could most likely very easily get a order for visitation of the child
If you go though court, or if he will agree, perhaps make it though a couselor to start, where each visits separately at first, and then when ready they meet though them. And if the dad is really wanting a relationship, can build it from there.

So it is not as much, should he, but how will it be done, since there is little that can be done to stop it , if the dad really wants a relationship and is willing to go to court for it.
And in court, he may get a lot more than you want to give, so if he is willing to make it informal for now, it may be to your best interest