If you can get away with unfined and unfiltered and you don't care too much about appearance, quite often the result is fantastic on the flavor end of things. Just like with wine, in the beer world there are people who don't mind cloudiness if they get all the good flavors they want from a beer. With my wine and with my beer, I prefer to go the unfined/unfiltered route if at all possible. The problem is that the masses sometimes find a cloudy beer suspect and won't give it the attention it deserves. So many commercial brewers will fine or filter.
That's the beauty of homebrewing-- brew what you like to drink, not what you like to see... because appearance really doesn't matter in terms of how a beer tastes.
As far as safety goes, there's nothing wrong with most commercially-available fining agents. IF you're not vegetarian, then there's nothing there that will offend. Most are non-chemical and derived from animal parts. I like BioFine.
I've seen an awful lot of vegetarians taking jello shots and not complaining about the poor horse that provided the gelatin. I always find that funny. Isinglass is fish-derived, so pescatarians don't have to worry ;)