“And to be entirely truthful, Jews have always looked down their noses at converts.”
Abraham and Sarah were converts, so no.
It is a specific mitzvah to accept and treat Jews-by-choice (real ones, with the mikvah and everything) the same as every born Jews.
A convert’s soul was present at Mt. Sinai and accepted the covenent, just like mine.
Sorry, I am not buying the Abraham was a “convert” story.