...if tomorrow most Jewish people decided to pray to Jesus, many Gentiles would be quite confused. Chaos would result whenever a Gentile interacted with a Jewish person.
At Christmas time, there are liberal Jews in the US , who buy and decorate Christmas trees, merely for the joy of celebrating the Holiday, as opposed to the Holy Day. Do most Gentiles worry about this? I doubt it...
However, I remember last Christmas, when the grocery man delivered our groceries to our door, I wished him a merry Christmas. He then looked at my Mezuzah, which was posted on the door post, and seemed a bit surprised/confused that I would say this.
So, I suspect as Foofie has stated, that some Gentiles are confused by the actions of Jewish folks. But why worry about it? I don't and if at Christmas time, my dog's Vet ( or any other gentile person )wishes me a merry Christmas with a doubful look on his/her face, I don't get anxious, red in the face or upset by it, I just say ,"Merry Christmas" back.
Why worry? Be joyful, have peace in your heart, and just try to get along with others as best you can...