It's quite a predicament, and I've been there before.
X was a friend of mine and we had been cool for years. However, X began to turn her azz wrongside out after she hit 20!

She became a real trip, and she did quite a bit of damage to her reputation. I mean, she was a Jerry Springer, Ricki-Lake-doorbell-ringing, "Oh no she didn't sleep with THEM", you-wouldn't-feel-right-leaving-her-alone-in-the-house-with-your-man kind of a trip. Now, I am not going to sit here and say that every member of a sorority (even, ahem, mine) is pure as the driven snow. A good number of folks are hardly as pure as some driven OVER or driven THROUGH snow...

However, many at least have the dignity and good sense to keep it on the d.l., you know?
But, I can't see letting a known, shall we say, "lady of the night" up in my organization. It ain't hapnin'... At least not through any chapters within earshot.
I didn't come right out and tell her, "You don't have a snowball's chance in h*ll of being an AKA cuz you're a big ole' stank-a-dank." But, I would never discuss it with her. When she brought it up, I would listen, and then eventually change the subject. She got the hint and stopped asking.
And although I know our sorority is the only way, Soror AKA2D, I wouldn't wish an underqualified interest on another organization.

That ain't right! lol