reading through your post, i can't help but think you might need to analyze yourself before you start judging other people and who is fit for your sister. Approve or not, you're not her keeper nor do you have any say over who she shoudl be with, even if you ended up being right in your judgements, it's best to keep them to yourself.

something that was very telling in your post:
"My sister met his boyfriend at a local community college around 2010. Around 2012 my sister introduced her boyfriend to the family. His appearance was not something I liked. He had a nose ring, an array of tattoos on both arms, and large black stud earrings. He pretty much looked like one of those hipsters/goths type of guys."

Even before looking at him on fb or did any of the "research" into this guy, it sounds to me like you already had him pegged. you arleady wrote him off before you even knew his behaviors, record or anything. He wasn't going to win any awards with you in the first place. The behaviors you didn't approve of subsequently just solidified your judgemental view of him. That's how I see it.

Keep your standards as your own and let others choose their own, just because you feel something shoudl be one way, another person may find those things unacceptable, or vice versa.