Imaofthree
I dont see why a Rabbi must mention it at all and who is she to “tell the Rabbi” what he should be mentioning. He is the Rabbi for a reason, he knows what the kahal needs to hear be it a dvar Torah on the parsha or a dvar halacha or whatever.
Additionally, we have enough things going on in our own communities to say Tehillim for. If you want to say Tehillim for them go ahead but it has never been the minhag in klal yisroel to say Tehillim for non Jews brabim in shul. In fact most shuls only said Tehillim brabim during the rocket barrage issue in eretz yisroel. So it would be extremely strange and unhear of to be saying Tehillim in shul for them. Lets be busy with our own issues. There are enough non Jews (311,591,917 million people living in the USA) to say psalms pray and give charity for for them. They dont need our Tehillim.