More generally, since Christianity at least is at heart an evangelical "share the Good News to all" religion, that a believer feels obligated to do exactly that has never been a problem for me, nor do I take offense to it.
Logically, it is up to believers in god(s) to make a positive case for belief in their god(s) to the exclusion of all others. That typically is a tough hurdle, which is why so many defenders of particular god(s) prefer to restrict their argument to their faith vs none at all atheism, rather than a far slipperier comparative religion defense.
The older concept of an atheist being someone who does not accept a particular god (even if they believe in some other) could include such religious "atheists" in that sense, but that isn't how most people use the concept today.
The term does naturally presuppose some manner of godly faith (rather than, say, a naturalistic "faith" that the rules of nature operate regularly throughout the universe).