Hi Health.
So basically, your answer is to not be friendly since these muslims are just waiting to literally stab a Jew in the back, chas v’shalom.
I am no fan of arab muslims, but I have heard more than one story from Israelis about arabs they were friendly with and worked with in Israel.
My parents, too, have this egyptian friend who was their car salesperson. This guy is still friendly with them over the years and brings over gifts and stuff from egypt and calls kibbitzes with them. I dont get why either one of them bother, but its true.
I guess if these neighbors are friendly and showing their baby, for the frum neighbors to get a little baby gift would be a huge kiddish Hashem.