Wow...I hesitate to say anything here...in some ways I agree with or at least understand all the viewpoints shared, conflicting as they are...and they are all valid, depending on the situation.
Once upon a time I was that Non-Scientologist girlfriend...so I understand this from the other person's perspective...
I know everyone's situation is unique. For me, a lot depends on two things...how long have you known her/actively dated her, and how well do you know her? How much are you emotionally invested in this relationship? Do you want to marry her? Live with her? Or is this a little more casual of an involvement than that, more a girlfriend for right now, "until someone better comes along", or "we're just living in the moment" kind of thing?
The advice I would give you would be very different depending on your level of involvement with her and the type of relationship you have, or that she thinks you have, together.
She is confusing Scientology with Christian Science, a pretty common mistake, which tells me that she is not really interested in either or much of a deep thinker on the subjects of religion or spirituality, or cults... Most people aren't so that's nothing against her.
It is telling, in a way, that you are witholding this from her, because you don't want to have to talk about it and answer her questions and deal with all the emotions that doing that will stir up for you. I think maybe you have a bigger issue to deal with regarding putting Scientology behind you...it's a good sign that you have gotten to the point where you can laugh about it with your folks...but you still aren't ready to be fully honest and open about your time "in" the Cult.
I understand wanting to compartmentalize it away from most of the rest of your life and friends, that's a pretty good coping mechanism for getting on with life. But you will be better served if you do deal with those feelings you are avoiding, eventually, once you are in a good strong place to do so. But if you do see a future with this woman, then you should tell her, only choose the time, place and circumstances so that they will serve your needs, and not totally blindside her.
Talking about another high control group might be a very good way to start off a conversation about it, one with a similar bad reputation like the Moonies. Watching a vid like Steve Hassan also...you can judge her reaction a bit, and then decide how much or when to tell her, or even if you want to tell her at all.
Just to give fair warning about her possible (probable) reactions...if she is anything like a normally socialized woman...once she finds out that you have "hidden this from her" and are reluctant to talk about it...she will want to find out all she can about it (maybe even come on this board) and "help" you with your emotions about it. Women love to talk about emotionally thorny or complicated subjects, and to "help" their partners with their problems. So don't even go there unless you are very willing to talk it over with her quite bit and answer all her questions, etc., until she is satisfied. The wisest course of action for you would be just not to bring it up.
If something happens and she questions you directly, then yes, do be honest about it, don't lie to her.
Chances are good that if and when you do tell her, she will feel hurt/puzzled why you took so long to tell her if it was "no big deal" in your life, and it's all in the past, etc. She might question you about the other kinds of things that boyfriends might hide or withold from girlfriends, such as...ever been arrested? Spent time in jail? Ever done drugs? No DUIs? No mental illness? Never married before? No kids?, etc., which is a normal and natural reaction. She may very well wonder, gosh, if he hid something this big about his life, what else isn't he telling me?
So be prepared for a reaction, even if she is normally a nice sweet girl, of the Spanish inquisition...her friends/family may advise her to do a professional background check on you, etc. She will talk about this with her friends, that's normal. Be prepared for her to feel upset over your not mentioning it sooner...it is a lie of omission. It will be normal for her to feel betrayed/hurt by your not telling her something of this magnitude.
Also, even though you are making light of your involvement here, a lot depends on how long you were in, that you were in the SO (pretty deeply committed to the Cult) and what kinds of activities you did while in.
Who knows, maybe Auntie La La is right, and she is witholding some things from you, too...
(She could be OSA!
)
The time to casually mention it is gone, would have been when she told you about the first call or contact she got from COS.
With luck she will have a compassionate response if you let her know that your primary reason for not telling her before was embarrassment. I think you have some unresolved feelings about your time "in" which you need to deal with to be fully free, but you can do it on your own timeline, so long as you don't gunnysack this forever.
I think on some level, if you really trusted her as your good friend, and knew her well, you would have told her already. So maybe your commitment to a relationship with her is not all that deep. Maybe that's something you should take a look at? I don't know how long the two of you have been "together". Maybe the relationship is not serious enough for you to tell her, yet? Do you see yourself with this same person six years from now?
Only you can answer these kinds of questions, and can decide what is best for you to do.
That you are reluctant to "rock the boat" now, as you are enjoying more of a normal life, tells me that you are not really ready to talk about it with a girlfriend...and that you have some more healing to do before you are more comfortable discussing it.
So grant yourself that time, if that is what serves you best.
Keep reading and writing here, if it is helping you.
Good luck to you, with whatever transpires.