I highly doubt anyone in this game is going to go around looking people up and then laughing at them because their levels aren't high, or something of that sort. Should that even be an issue, the blacklist feature works quite nicely.

OP states that members of his LS knowing what class levels he has leads to drama. There aren't a large variety of reasons for there to be LS drama over a player's levels. It isn't difficult to guess the scenarios as to why he would want to hide them. None of those scenarios merit the addition of a feature that would allow anyone to hide their levels.

There may be good reasons. Fact of the matter is, there are no reasons good enough to make up for the bad side-effects.