Wedding plans, but husband to be hasn't been introduced to my father

The maid of honor choice isn't the only dilemma I have.

I have never introduced my partner and my father to each other. We have been in a civil marriage for 10 years and have had two children during that time.I don't feel good about it, but I don't know how best to deal with the situation, so I avoid it completely.
My father emigrated after separating from my mother about 12 years ago and remarried there abroad.The separation was very bitter and my father caused my mother a lot of suffering over the years, which is why I took sides, even though my mother never wanted it.At the time I met my partner, the contact between me and my father wasn't that regular and since he lived abroad, I didn't think it was that important to tell him about my boyfriend.My father comes from a culture where there are no such things as long-term partners. You're either married or single.Despite the strong faith and upbringing he has experienced, he is very liberal compared to his siblings. My uncles and aunts frown on me "walking around" without a headscarf and there used to be a lot of pressure put on me.
At least my partner and I are getting married soon and a lot of people think it's weird that they don't know each other.
I deliberately avoid the situation because I don't know how both parties will react to each other. My father has become heavily religious since his stroke and is always admonishing me about life after death if I don't return to (practice) my faith. I forgave him after the stroke and we became close again. Despite the physical distance, he tries to establish a relationship with his and that's why I turn a blind eye.

At least my partner isn't religious at all and doesn't think much of religions. My partner respects religious people and he has kept a few customs, but he sees religions as pure instruments of power for people.
My fear is that my father will not like it at all that I am marrying an "infidel".
I told him my partner is Muslim to reassure him, but I'm sure he would know that at least my partner doesn't practice it.I could at least "pretend" but my partner doesn't pretend. For example, he would admit that he drinks alcohol. I do, too, but I don't admit it to my deeply religious relatives.
I can already feel some eyes turning at this text, but it's a bit different in other cultures. You don't want to be banished from your family. When people tell me they have little contact with their family, it sends shivers down my spine. It's bad enough that I don't have any contact with my narcissistic sister... (dilemma number 3) but I don't want more people to be either.
I know my father would show that he doesn't like the fact that my partner isn't religious. And that would be really uncomfortable for me.I'm also ashamed of the wife.My mother is an educated, accomplished woman, and his wife is not brightly exposed. She has a hard time expressing herself properly and has let herself go a lot over the years.I would like to visit my father with my future husband at least once, but my father's wife has no idea how to run a household. It's not dirty there, but chaotic. My father is physically severely restricted due to the severe stroke he had. Despite everything, I'm grateful that she takes care of him.
I fear that both my father and my partner will look down on each other.I don't want to see it "live" or feel it. And rather live on in the lie:
I tell my father that my partner is often away from home for business reasons (my partner does travel a lot for business, but not as often as I say).
And I tell my partner that my father is not able to have visitors that often because of his health. In fact, my father often goes to rehab etc., but these are just excuses on my part.
I just don't want them to meet for fear. I want to spare both of them the experience.Maybe I'm imagining it all much worse than it is.What do I do now before my wedding? Do I introduce them to each other and if both of them don't like each other afterwards, then I have to accept it like that? How do I jump over my shadow?