My church is non-denom. I didn’t know about this until I saw your thread. We aren’t doing anything with it.
I guess it’s not really an issue for us because the main premise of being non-denominational is that unity in Christ is all-important and unity within a particular denomination is completely unnecessary. It’s totally fine if you do it, but you don’t have to.
Additionally, my church is relatively non-ecumenical, at least on paper. The senior pastor in particular and the leadership in general is a lot more so, but it’s not like ND churches have a bunch of fractures that need to be healed. I tend to think of these kinds of things as a series of visits to the doctor to get a cast put on a broken limb followed by trips to the community therapist in order to resolve points of conflict. ND churches don’t have these same kinds of issues to work through. Who exactly is it that we would have to work things through with? I can’t think of anyone. **There’s far less motivation to repair our relationships with other groups of Christians because there’s not really anything to repair.
There’s also something to the idea that the non-denominational ideal is about as far removed from the inter-denominational ideal as you can get**. So my church isn’t really concerning itself with this week of prayer for Christian unity. We have other stuff going on, and a lot of what motivates one group or another to do this kind of thing just isn’t applicable in a ND church.