In my humble opinion, which is based on some personal experiences, I would not even socialize outside of the workplace much less go to a non-muslim place of worship or eating their food. This is especially true if you have a growing family with teenagers. This apparently benign socializing with non-muslims can end up where you have to accept a non-muslim son or daughter-in-law. Some people are very liberal in this respect. Please find out where you and your family would stand if that ever happens to you. Also, be mindful and cognizant of who your children associate and socialize in their extra-curricular activities.
Very Sincerely yours.