I am a registered sex offender who is dateing a woman w a young daughter and her ex who she shares custody with is telling her that he will take her daughter away if we continue to date. Is the fact of this alone enough to give him ability to take her daughter away?

This ( or any change) is enough for him to take her back to court to ask for a modification.

If he can win is another issue, So she needs to be discussing this with an attorney.
The real issue in my opinion will be why you are a sex offender, at 18 did you have sex with a 16 year old ? Or did you molest a small child, or expose yourself to children The why you are an offender is the real issue and will be the issue at custody hearing.

If her ex can show the courts that you being near the child could be a threat to the child, yes he can take custody away from her.