Plenty of options
There's no shortage of agents who handle lit fic, and some do so almost exclusively (at least as a share of their fiction sales, that is): check out somebody like Betsy Amster.
There are also a bunch of well-regarded smaller presses that specialize in lit fic (like Greywolf), and you don't need an agent to go there. Even MacAdam/Cage, which no longer really qualifies as a small operation, still takes submissions across the transom.
It's common to hear folks bemoaning how hard lit fic writers have it, but many, many agents handle at least some, and many major imprints keep their hand in the game even if it isn't their specialty.
The good news about lit fic:
--despite all the whining, there's far more places to sell it than most genre fiction.
--there is less fretting over whether or not your 'product' fits some template that publishers believe will sell.
--acqusitions people have more leeway and their tastes tend to be more idiosyncratic.
--you don't need an agent to approach some of the most respected players.
The bad news about lit fic:
--you are unlikely to receive large advances or see your book on the tables at Barnes & Noble (but you knew that, right?).
--those idosyncratic tastes which mean someone out there will embrace your book also means that most of them, be they agent or editor, won't like it. So expect to spend a lot of time finding your soulmate.
As to your possibly objectionable content: you can look for folks who claim to be seeking 'edgy' material, but this is more often posturing than realistic self-evaluation. In the case of editors, see what they've really published. In the case of agents, see what they've really sold. But if your work is one of a kind, you'll just have to get out there and get your pole in the water. Good luck.