I would want to meet a new girlfriend of his if she was going to be living with him and taking on a parenting type role.
There have been a few threads about this recently. It's not unreasonable to wish to meet a new partner if they are going to be in contact with your children but that's all you can say about it. It's your wish and it's not unreasonable.
BUT it's not your RIGHT. The same is true for him. So to answer your question:
Is it reasonable for my ex to demand to meet my new boyfriend?
NO. A big fact NO. There are no demands here.
If you are split up, that's it. He has no right to demand anything at all. If he wanted input into your life and who your partner is, he needs to be in a relationship with you.
Don't forget that in situations like this there is a third person involved - the new partner. It is perfectly reasonable for them to take a stance of "No I'm not meeting your ex. They are nothing to do with me and I'm not interested in your drama or being vetted".
Think about it - it's utter crap. What if he doesn't like your new partner? So what? He can't stop you seeing him. He can't stop the children spending time with him. To do that he'd need to get a court order - which he won't get.
Tell him to f*ck right off. Having said all that, if you are likely to want to meet a new gf of his for the same reason, a bit of diplomacy here may not go amiss.