You are going to have that issue with any religion that follows the advent of your own. So it doesn't apply backwards to Jews, who were here first.
Personally, I think an individual's relationship with God is very personal and unique. In that vein, if a Mormon considers himself Christian, fine. That doesn't invalidate your faith as a more mainstream or traditional Christian at all.
Doesn't mean it's not common. My Episcopalian mother has trouble thinking evangelical Christians are truly Christian, because they don't practice Christianity anywhere near the same way Episcopalians, Catholics, or more historical denominations do. She doesn't get making up a church, its own statement of faith, and not following traditional Christian creeds.
And many Sunni and Shia Muslims have a lot of trouble with
Ahmadiyya Muslims, which is a newer sect with some significantly different beliefs. I believe you will find Orthodox Jews who don't few Reform Jews as "truly Jewish" as well.
FWIW, I teach my child there are many different religions across the globe. People are free to choose what they want to be, or free to choose to not practice religion at all. We hope that whatever a person chooses helps them be a good and kind person. No religion is one size fits all.
This is also a helpful belief for him when other kids try to convert him to "their" family's religion, ,which happens far more often than I ever would have thought.