The best way to treat this, and avoid it in the future, is to call around to
vets/pet groomers, and ask the prices for trimming of the cat.  Our vet did
our long-haired kitty's behind at no charge (because we are good, paying
customers).  While she looks a bit silly, having the backs of her legs, the
rear-most part of her belly, the underside of the base of her tail shaved
(not completely bare, but down to just-shorter-than-a-normal-cat's-hair
length), she no longer gets poo caught in her fur.  She looks normal, until
she gets up and walks away - then she looks funny.

Don't use scissors - you could accidentally nick her skin (ouch).

Not that I'm aware of. I have 3 cats, the youngest is especially furry. So,
I have to trim his butt. Yes, I take scissors and cut about an inch of hair
all around his but so he doesn't get litter in his hair. He's black so the
only thing that worked was cutting his hair. He finds it confusing, what I'm
doing to him back there, but he tolerates it pretty well. Using water
doesn't work, his black hair showed the litter never left it so I had to cut
off some of his hair. Now I just keep him trim. He's such a fuzzy creature
you can't even tell I trim him!
He's a domestic long hair, not a persian. He sure is furry, though. I don't
think there's anything wrong with trimming the hair around the groin area.
It keeps them cleaner and you don't have to worry about future problems.

I have longhairs, too.  Birmans (the Sacred Cat of Burma).  You might
try changing litters.  I use Worlds Best Cat Litter and it is
flushable--the clumps fall apart when dumped in water.  Therefore, it
should be easy to rinse out of your cat's fur....

Lisa....  :-)