If the game itself allows you to mechanically be a class/job/race/member of a faction, you have all the right in the world to use that in your roleplay. The problem with the Jobs is that, as you said, most of them are introduced as being incredibly rare. Roleplayers have to come with a handwave for why every Player Character can be a "very rare" White Mage (or whatever Job) despite of what the lore says. My personal take is that the jobs have been reintroduced into Eorzea for some time now, but not terribly long. Since all (or at least most) of the Job and Class quests exist in their own vacuum, not interacting at all with the main storyline (except for the odd cameo, like in the Summoner's last quest), it is safe to assume that, for example, the Padjal have been accepting and training new White Mages for a while. The same applies to everything else. Some Jobs need more thinking about how your character came to be one, but they are all perfectly doable.
How they are treated during roleplay depends on each player and character. Some people might decide that you absolutely cannot be <insert Job here> because the lore states that they are extremely rare or dead. Others might decide that it's alright as long as your personal backstory isn't a copy-paste from the storyline presented in the game itself. Others might not care either way.
If the Black Mage storyline states that they are feared, then chances are other player characters will react according to lore. Or not. Again, it's something that depends a lot and you should probably not worry much about what their reaction will be.
How they are treated during roleplay depends on each player and character. Some people might decide that you absolutely cannot be <insert Job here> because the lore states that they are extremely rare or dead. Others might decide that it's alright as long as your personal backstory isn't a copy-paste from the storyline presented in the game itself. Others might not care either way.
If the Black Mage storyline states that they are feared, then chances are other player characters will react according to lore. Or not. Again, it's something that depends a lot and you should probably not worry much about what their reaction will be.