What an interesting thread. I'm new to it, just read it all then.
When I read the OP I wondered whether the poster was male or female, but reading on I can't see how it mattered. The Op said their DP had some historical issues with faith that couldn't be elaborated on- What those personal issues are is irrelevant to the question the OP was asking (how important is Sunday worship to fellow Christians).
Edith. Kudos for your patience in what sounds like a tough situation for you both. My two cents worth:
Regular attendance at a community gathering at a home church (on whatever day- ours is Sunday) is really important to me. Theologically I believe it's important and is encouraged and endorsed throughout the New Teatement as being valuable and a key way to grow spiritually, be encouraged, and encourage others.
That's not to say that God doesn't care for and encourage those who cannot for whatever reason, meet with other believers (obviously he does - so many amazing stories of persecuted Christians). And maybe, if you can't find another way forward with your DP, you might need to make loving sacrifices for your DP and not meet in the ways the NT encourages - and if that's the case (somethings between you and God and your DP, so I can't say), then I trust that the Lord will sustain your faith in other ways...but it IS important and I do think you are right to do all you can to work towards being part of a church community.
That said, I believe that church is a community to belong to, not an event to attend, so there should hopefully be ways you can connect with a church community without having to attend on Sundays. If your current church doesn't have midweek home groups ( sorry I can't remember if you said it did), then maybe you need to find one that does, so that you can get to know the church members without regular attended nice on weekends. There are a w members of our church who come very irregularly on Sundays, but attend weekly or fortnightly home groups and other social events, and are loved and included as part of the community in other ways. Having said that, I wonder how your DP would feel if you were to begin attending social events with your Christian friends? That might be just as hard.
Bertram - not sure if you're still reading or have...we...left the thread...but to your point about it being a big issue if your DP became a Christian, I quite agree with you - but not because I think it would be a change from being a rational to non-rational person (I don't believe Christianity is without evidence, but that's another thread;-) )
I'm a Christian- so is DH. If he were to suddenly renounce his faith that would be enormously hard for me, because faith is not just a hobby or interest but a worldview - more than that - being a Christian (ie having a relationship with God through Jesus' sacrificial death) is the most fundamental aspect of who I am. I wouldn't leave DH is this were to happen. But it would be devastating for me because he would be fundamentally changed at the core of his self- and, whilst I would still love him, our relationship would be very different.