Not a direct analogue to the OP’s situation, but I feel like talking and you can’t stop me.
In mormonism and presumably various other religions, there’s a fairly standard practice of having one person say a prayer aloud while others listen quietly, with the implication that that person is speaking for the entire group. So the speaker is “praying for” the group - he’s praying in place of them, on their behalf. (Rather than for their benefit, as is happening to the OP.)
I happen to consider all forms of christianity to be demon worship, quite literally. As I got older and this opinion crystallized I became more and more uncomfortable with being present during such prayers; by being a member of the silent group I was being implicitly included in the group of people who were praying - the group worshiping the demon. And while it’s not my business if other people are worshiping demons I don’t like doing it myself.
Of course, there’s an easy way to avoid this - don’t be part of such groups. When such a prayer is threatening to ensue, one merely needs to leave the room and get far enough away to not be part of the group. (Getting out of earshot is a good start, though I like to also have a closed door between me and them.)
I ran into a snag, though - my family is mormon and when I expressed a desire to exit the room during prayers, my mom refused to let me leave. Making it quite explicit that she agreed with me that being in the room was making me worship, and that she wanted to force me to worship against my will!
So how did I respond to non-strangers insisting on praying for me in my presence? I saw little choice but to refuse to even go over to my parents’ house at all, until she relented and allowed me to leave the room when a prayer ensued. (Yes, I was an adult at the time, with my own place and everything.) She held out for over six months, before relenting and saying that she would allow me to leave a room.
Yeah, I’m still pretty sensitive about this. So to the OP’s situation, if a stranger offered to pray for me, my response would be “How about you don’t.” Followed closely by “How about you don’t and fuck yourself with a rusty chainsaw while you’re at it” if they didn’t take no for an answer.