Certainly be at peace praying with any group that prays in ways or words similar to what we use, even if they do it a little differently. Who cares if they attach parts in different places or say “debts” instead of “trespasses”. The intention is what matters here. You’re not invalidating a Mass or doing something illicit since you’re not in a Catholic liturgy. When in Rome… (well, in this case, er, well…you know).
The only things I would give pause to or completely refrain from is (1) communion, and (2) prayers directly contrary to our faith (don’t join them in praying that “those Catholics may soon see the errors of their ways and be saved”).
Sometimes, you just silently observe and don’t participate or assent with your “amen” if you feel their intent may be ‘iffy’ in Catholic doctrine, such as “Lord, we know his baptism was just a symbolic act that cannot save, for works cannot lead to salvation, but he answered the altar call…” Sure, they may be technically correct about certain aspects, but they’re back-handedly smacking our doctrine in the face.
Bottom line: don’t sweat the small stuff, and when in doubt, just maintain a respectful silence. That’s my :twocents: