Hm. It's possible that I've lost the thread of what we're discussing.

It seems to me to follow from what you've said that a theist who explicitly believes their belief in god is unfalsifiable, therefore necessarily explicitly believes there to be no evidence for that belief, therefore necessarily believes that proselytizing others is necessarily futile (since everyone requires evidence to adopt such beliefs, and therefore they believe that everyone requires evidence, and since they know they have no evidence, they know they cannot convince anyone), therefore is functionally equivalent to an atheist, who is functionally defined by their unwillingness to proselytize.

Have I followed that correctly?

If not, can you provide a corrected summary?