This is of course the WELS position in contrast to LCMS. Also, it should be noted that although it was never clearly defined, this was the position of the great synodical conference. LCMS just moved away from it with their acceptance of the boy scouts, among other things.
Now I personally do not agree with the WELS position. I have prayed with my advisor at Marquette who was Catholic and also with Reformed friends (as well as ELCA friends) and I do not consider it to be objectionable. If I share an evening meal with someone and pray to a God who we commonly accept (based on a common acceptance of creedal orthodoxy), then I am not really saying "hey, we agree about everything, so why all this division from the Reformation?" All I'm saying is "hey, we both accept the same God who the creed talks about, though we have serious differences about what he has done to save us. Nevertheless, we can be thankful together for the fruits of creation." Communion fellowship I think is a little bit different since we are "proclaiming the Lord's death until he comes"- meaning we are claiming that we have a common accepted understanding of what the Lord's death means.
Nevertheless, one of the things I consider to be the weakest about LCMS theology is that we haven't really thought through this issue enough. That's why there was the whole big problem with the Yankee stadium event. Where do we draw the line with prayer fellowship? I mean, obviously we can't prayer with people who aren't Christians (creedally I mean). But where do we draw the line even within creedal orthodoxy?
Does anyone have an opinion? (I'm certain you do!)