Avira, yes, OC 215 seems to have Rema saying the opposite, and more of a discussion later on. Also, an argument whnether kuti here is a substitute for a non-Jew or a min in general. Sh’A harav has a discussion of a min, probably a code word for a christian. Bottom line, attendees of such rallies should have halachik guidance in advance on when and how to respond. In my humble experience dealing with friendly and helpful people from other religions, they do not engage in sneaking their brochos into conversation. Those who do are obnoxious l’hathila.
But all Sh’A discussions are about literally blessings. What about answering amen or other types of agreement with reasonable statement (I presume that is what it was as you are not taking an issue with his statement).
Someone comes to you and says “Am Yisroel Hai”, can you answer Amen? Yes? Sure? Does amen carry any implication of religious unity between parties? If yes, is it because we give significance in this word, or because preachers use this language?
As to a bigger issue – I understand R Soloveichik paskened that cooperation on religious issues is osur, but ok and desired on social issues. It appears from the above that more guidance is required when actually implemnting such policy. Can someone ask these questions from the poskim that supported the rally?