Congratulations thirti4thirty on your next educational step! I hope you find it exciting and rewarding.
I have to agree with Quiet Ballerina. I have a Ph.D. and while I encountered some pretty significant challenges along the way, I don't regret doing it for a moment and honestly, I never really thought about how it might affect my personal relationships one way or the other so I'm interested in reading others' responses. I also work on a university campus where you can't "swing a dead cat" without smacking another Ph.D. so admittedly, my response is probably skewed.
Earning my Ph.D. was about having the hunger to learn and to stretch and challenge myself. And yes, I knew it would help my career prospects in the long run. It was all internally motivated; I competed with no one other than me. So while I have the degree, I rarely think about it and it rarely if ever comes up in conversation. I'd like to believe that I would be equally confident without it. With that said I know a few folks who never like to let you forget about the letters behind their name. Sure, if one uses their degree status (or number of) as a weapon, it will turn off lots of people regardless of romantic interest.
I find intelligence (whether it comes with a degree or not) super sexy! A man who is confident and self-assured with what he brings to the table won't have an issue with your degree and/or intelligence. Interestingly, I worked with a professor who has gone on to be a Dean at a prestigious research university. Several years ago she waded into the online dating world, met a lovely man who is a long-haul truck driver. No degrees. They have a son and remain happily married.
As Quiet Ballerina states, don't limit yourself.