Others who see more differences than similarities take offense to the term.
That's not really why I take exception to it. I take exception to it because it strikes me as a construct onto which specific denominations (or Christianity in general) can deflect responsibility. Its origin as a term had only the best intentions.
If you mean the term has been used to deny responsibility of Christians for any anti-Semitism in the past, I haven't seen it used that way. The use of the term that I find problematic and has shown up in the past few years is when it's used to suggest that Islam is something inherently foreign and opposite to a shared Jewish-Christian tradition. In any case I don't think it makes sense to use the way a term has been misused as a reason to automatically dismiss the idea that people are trying to get across.