It boggles my mind how my conservative father even remotely thinks anything positive about star trek, let alone being obsessed with it.

Steve absolutely nailed it. Though I think his 4th point about optimism being a core part of star trek was missing a subsection. Almost all of the characters, and especially the ones the show wants you to root for have shit loads of empathy for the people around them, and often times it even extends to outright enemies.

Whenever a crew member is losing control of their behavior because of a mind control space entity, the crew's first reaction is a level of concern people only have for close family members. When Sisko is doing arguably immoral acts for the greater good, he is wracked with grief and empathy for those he had to hurt. Janeway on the other hand just wants her coffee lol.