Taschlich with Christians?

I attended RH services at a new synagogue I’ve been going to. During our afternoon Taschlich service, some Christians from the church across the street joined us and my Rabbi said it was an annual tradition for them to do so.

Is this rather common—including Christians in Taschlich? I guess it leaves me with a bad taste in my mouth given all the ways in which Christians have tried to erase Jews and Judaism while culturally appropriating Jewish traditions later. I’m not sure if I’m being overly sourpuss about it.