Well, I will have to find the little booklet I was given a few years ago on WELS and fellowship by our pastor, but from what I'm guessing now, they would take issue with joining with the RCC on just about anything -which I think is sort of ridiculous in some ways. I like the LCMS much better on this issue. On this issue we are not in any way saying we agree with all doctrine we are just joining in a common cause. I think the WELS is even stricter than the LCMS on things like this.
We are not allowed to even pray at public events with other(non Lutheran) Christians, or attend things that do not specifically pray in Jesus name. Now the WELS does consider RCC, Orthodox, Baptists, ect, to be fellow Christians that teach most of the truth but that have let error creep in to their teachings(per our church) so no fellowship. So not like some super fundamentalist churches that think the RCC is the harlot of Babylon or something.
I was given this booklet by our pastor when my then middle-school aged son wanted to attend am overnight para-church outing with non- Lutherans, that would include some scripture study, ect. Personally I had no problem with it as my son was well versed in what we believed and would not be swayed as he attended our parochial school and it was just an overnight thing. (So I let him go). I think our Pastor was concerned ( and with some validity) that he would be swayed into the Anabaptist way of seeing salvation. I figured it was way better than some of the things he could be involved on an overnight trip.