But how does homophobia and misogyny within the Mormon church affect people who aren't in the Mormon church?

Also I find it telling that you say "the church earned that reputation". Yes, the church, not a single man. The leader of a church is rarely a king who can change doctrine on a whim. If this man had repented of homophobia and misogyny, he may well have been supplanted by someone else the very next day. So among the many things wrong with the wording of this obit, the fact that they call him out personally as homophobic/misogynist rather than something more accurate like "under his leadership the CHURCH was homophobic/misogynistic" is a big one.