I agree with those who have said to talk to the mothers, but I really do believe it is in your best interest to tell them that your son is on the spectrum. Tell them that you are grateful that he is high functioning, but it is a work in progress with his attitude with his parents and you would appreciate it if they could at least try not to be so hurtful.
You do need to understand that there are parents who don't discipline their kids and are bad parents. People don't like that. You should know also that there are parents who try their best to discipline and deal with their kids, but their kids are very difficult. Those parents care and try, but still struggle. Those parents who have easy children will never understand what it's like to have difficult temperments to deal with day in and day out. And this is neurotypical kids I'm talking about. So you are NOT the only parent that goes through this...
The ladies here are absolutely right in telling you that you need to work on transitions with him. Seek out your doctor to get some help.
With a child on the spectrum, you will always have to deal with judgmental people. But more than that, your SON will have to deal with judgmental people, for the rest of his life. I know a young man who I see every week who is very smart, very talented, handsome. BUT when he gets upset, misses social cues, something happens that he doesn't expect, and many other "triggers", he blows up. It's ugly! I can't count the times I have had to take him aside and lovingly talk to him about his behavior. And I have to go tell other people that he is autistic because he has hurt them by blowing up at them. Everyone knows how smart and talented he is, but sometimes even knowing he is on the spectrum, he isn't very well liked by people who aren't close to him. Thankfully he has a girlfriend now who really has worked hard to help him keep calm, but she can't help him while he is at work. I have met his parents, and they are wonderful people, calm and patient and loving. They have done their best. He has been living on his own for 4 years, and this is the best that they could have ever hoped for.
And this is YOUR end goal as a parent as well, working towards him being able to take care of himself one day. Getting your son to learn to transition better is your most important immediate goal, over the issue with those moms. But if they are nice ladies, they will be more understanding if they know he's on the spectrum. If they continue rolling their eyes, knowing it, then you don't want to have anything to do with them anyway.