I once dated a Christian who said she didn't respect me because I'd never be like a certain evangelist who, to this day, is one of the best men either of us have ever been blessed enough to know. Was this a relationship I should have pursued and stayed in?

No. God tells us, "Each individual among you also is to love his own wife even as himself, and the wife must see to it that she respects her husband." (Ephesians 5:33).

If a relationship lacks respect, it's not one to be in. Move on and find someone where both parties are edified and bring glory to God.