Can a Cohen marry a bat niddah? Are Cohens generally restricted from marrying baalot teshuva because of the possibility that they may be b'not niddah?
The Shulchan Aruch Even HaEzer 4:13 says that a ben or bat niddah is 'pagum' (defective). The Beit Shemuel, Chelkat Mechokek and Gra (the major commentaries there) all say that this does not exclude them from marrying a kohein.
I've never seen any restriction brought down in halacha that would prohibit a Cohen from marrying a Bat Niddah.
Moreover, the application of Ben/Bat Niddah has been severly downplayed by 20th century poskim.
The Steipler Gaon: The concern regarding a ben niddah's character is merely statistical. If an individual shows good character, he is obviously an exception and the warning can be ignored.
Another opinion cited by the Steipler Gaon: The blemish of ben niddah is hereditary for an infinite number of generations, not just one, and in fact all of us are likely to have it (or some other blemish) somewhere back in our lineage. So we're all on equal ground and have no reason not to marry each other.
Rav Moshe Feinstein: In many cases we can't be certain the mother was truly a niddah mide'oraita, because maybe she went swimming after her period in a body of water that qualifies as a mikvah, and thereby became tehorah. (Rav Moshe does not discuss the fact that she would most likely have been wearing a tight-fitting bathing suit at the time.)
(All of the above quotes come verbatim from here , although I have learned them originally elsewhere)
The last point about not being a "niddah mide'oraita" is significant: Technically, a woman must have r'iah (seeing) AND hargasha (an internal sensation) to qualify as an actual niddah. It could very well be that in our times, no woman is ever a Torah-level niddah.
So one on hand, we still treat the prohibition of sleeping with a niddah very seriously, because even the possibility of kares (spiritual excision) is a serious matter.
On the other hand, AFTER THE FACT, there are many reasons to say that no one is truly a ben/bat niddah nowadays.