I wouldn't stand for this OP. If you think it's not going to change I'd get out now.
I had a very very similar story with my now husband. When we met he and his ex (together for a decade, never married , no kids and no reason to still so entangled) had been broken up for around 7-8 years but we're living in each other's pockets. He spoke about her all the time, they texted all the time, he looked after her dog for free several days a week (he works from home) and on one lovely occasion he left me sat in a restaurant eating a meal on my own (which I was treating him to!) to go and answer her phone call, and was gone for 20 mins.
He also still lived in the flat they had shared together and her shit was everywhere! Things she had made (she was crafty), her belongings lingering at the bottom of cupboards, cards she had written him in the lying around in kitchen drawers.....
And I couldn't say a bad word about her. All his friends loved her, and if I ever expressed annoyance at the any of the above I was branded a jealous cow by my DH as "XXX is such a lovely person, you are just immature. You are jelly and controlling. She is the kindest person ever i can't understand why you're being so horrible".
It literally drove me insane. Insane. And in hindsight now I put up with much more than I should have done for longer than I should have done. My DH had been single for years before he met me, was used to doing what he liked and has no real family, so old friends were very important to him, and I learned to understand this. But their friendship (in light of their history crossed a line).
It all came to a head when I decided that it probably wasn't going to change, and it was really damaging my self esteem, especially when my boyfriend (as he was at the time) would respond to my distress by assassinating my character and praising his ex. I realised it had to end when I literally lost my mind one night - I have never behaved like this before or since but I we had a huge row, I became hysterical and threw a jug she had made (that adorned his mantle piece) at him! It went past him and smashed against a wall.
I went home and collected my thoughts and decided that his life is his own, as is mine, and we clearly have massively different opinions on respect and boundaries. I decided (somehow after we'd managed to stay together for about 9 months!) that it was time to cut my losses and have some self respect.
I calmly told him , after a couple of days NC, that I respect his wishes but I cannot personally cope or agree with their extremely close platonic friendship. I never gave an ultimatum actually, I was 100% intending to end the relationship.
Over the next few weeks he seemed to have some kind of epiphany and contacted me asking to talk. Long story short he realised (finally) that his future was more important than his past and agreed to cut all contact with his ex. We have been together for 5.5 years now, have a lovely home and a baby on the way. When he moved from his old flat in with me I insisted that nothing of hers moved with him.
It's something that we never really talk about now, but it took a long time for me to fully get past it. We kind of agreed to disagree (he doesn't see her but I think if questioned would answer that it would it would be nice to maintain some kind of a friendship). For me, things had got so bad in the first 9 months, that I could only really accept him back of he went 100% NC with her. He made the choice and the gesture of doing so so I gave him another chance.
As I said he had no family that idolised her, but several mutual friends with her - who didn't like me and for a long time I was viewed as a complete bitch. They have all come round now.
I know my husband inside out now, and he can be a little insensitive emotionally and does sometimes need things making very black and White. He does really value his old friends and I suppose to him she was just one of these. As far as I know he hasn't even seen this woman, but to be honest he might have emailed her a bit or met for a coffee without my knowledge, and to be honest I don't even care anymore. She couldn't touch what we have now and we have totally moved on.
Long long posts I know... But I just wanted to share my story. I would end the relationship if change looks unlikely and (without blame) explain that you clearly have different boundaries around exes. If he has some kind of epiphany later on and realises what a twat he has been , then maybe you have a chance and can lay down your terms. But don't get your hopes up. I'm still amazed my now husband did the turnaround that he did.
But you have to put yourself and your mental health first . I know how damaging this kind of thing can be! You are not being jealous or immature, believe me!