While I'm away, readers give the advice.
On curbing proselytizers: I've faced similar challenges for decades, and developed successful strategies.
(1) As soon as proselytizing begins, even if you just arrived or just sat down for coffee, say, sincerely, cheerfully and without rancor, "Oops, religious talk, gotta go. See you later, Mom. Love you." And then immediately, with no other words, either hang up or leave. The quicker your exit follows the proselytizing behavior, the better Mom will see the cause-effect relationship.
Repeat this as many times as necessary. Dozens. If you do this faithfully, Mom will learn that proselytizing results in immediate undesirable consequences (your absence). I'm assuming she enjoys your company, is not in moderate or late-stage senility, and will tend to modify her behavior to extend the pleasure of your visit.
Try to do this in a way that will not embarrass Mom in front of others. Shaming her or fussing at her will slow down, and perhaps derail, the learning process.
(2) Learn to spot precursors to Mom's proselytizing, such as certain television programs, community or social events, or conversation topics. Once you've achieved success in stopping or at least reducing the frequency of her unpleasant behavior, then try to avoid being in a position where she can engage you when these triggers are sure to be present.
Once you start training her to not proselytize you directly, she may become rather sneaky about it — you may suddenly notice that the table blessing now resembles a mini-sermon, for example.
If that happens to the degree it gets to be a major irritant, remind her that her behavior serves to drive you away more than attract you (as a reader of yours suggested).
Another technique would be to keep a stack of literature about some interest you are very passionate about, and every time she engages in this behavior, turn it back on her. Be sure to do it in a sincere way, without rancor. "Since you are sharing what's on your heart with me, I must do the same. I feel as passionate about (blank) as you do about your religion, so I know you will want to hear me out, because you love me." And then deliver a two- or three-minute soliloquy about whatever, and don't let her get a word in edgewise. Put the literature in her hand, smile, tell her you love her, and then leave before she can respond. Do this over and over.
Though this technique might seem more satisfying, it actually isn't as effective as No. 1. Avoiding unpleasantness and moving toward pleasure is a more basic and effective motivation than getting insight through empathy. Some people aren't very able to draw parallels in behaviors and situations. To her, your passion about whatever — the environment, social change — is likely to seem completely dissimilar to hers for her religion.
(3) And then finally, most importantly, just learn to love her anyway. Even if she stops proselytizing, she probably will continue to fret privately about your lost soul. Don't let your angst over that become a mirror image of hers over you, lest the two of you become permanently engaged in some philosophical Kabuki.
Anonymous in Anonymous