I'm not going to judge your relationship based on this post because I'm sure your fiance has tremendous qualities that attract you to her on a physical and emotional basis. And I don't see many people commenting on their own journey with their spouse to convince them of the magic of FIRE, so I'll bite. Sorry for the long post.
I moved in with my fiance about a year into the relationship. Her money skills seem pretty close to OP's fiance's skills: she was contributing 10% to her 401k, no credit card debt, no mortgage debt, no kids, had $15,000 in savings, was making about $60,000 per year, lived in a small and very affordable apartment, etc. The only criticisms I could make was that she had a pretty hefty car payment ($350/month), either could have saved more or paid more towards or her student loans, and was investing in some funds with high expense ratios.
Before being critical, though, I hit myself in the face with a frying pan. Seriously stop and think about it. My then-GF was probably in the 75th percentile when it comes to financial competence. She had a Masters degree, was a licensed professional, and had been living on her own and doing just fine for about five years before we met. It would have been insane to be overly critical when she was doing so many things right.
I instead opted to be very gradual about everything. I did tell her I wanted to retire early, but I knew it would take time for her to figure that out. So I opted to read books together (she loves to read). I just looked at my Amazon cart from 2014. Our books:
(1) "I Will Teach You To Be Rich" by Ramit Sethi;
(2) "Total Money Makeover" by Dave Ramsey;
(3) "Why Didn't They Teach Me This in School?: 99 Personal Money Management Principles to Live By" by Cary Siegel;
(4) "Coin: The Irreverent Yet Practical Guide to Money Management for Recent College Graduates" by Judy McNary.
Our book list in 2015 becomes a little more advanced:
(1) "Your Money or Your Life" by Vicki Robin;
(2) "Bogleheads Guide to Investing" by Taylor Larimore; and
(3) "Early Retirement Extreme: A Philosophical and Practical Guide to Financial Independence" by Jacob Lund Fisker
I only list these out because they quite remarkably illustrate our journey of understanding money together. We've gone from just doing the basics right to really being smart about money. Since living with her (about 1.5 years now):
(1) She switched to an American Express SPG card with travel benefits;
(2) She moved her money market funds to Vanguard and invests solely in index funds;
(3) She inherited a decent sum of money and put every penny of it to her student loans;
(4) She upped her 401k contribution to 20% (about $12,500 per year);
(5) She opened a Roth IRA;
(6) We got our library cards and don't usually buy books anymore;
(7) Ditched her $40/month gym membership.
I'd still like to do more things. I'd like her to automate the bills. I want her to switch bank accounts from Chase to Schwab. I'd like her to max her 401k all the way to $18k and open an HSA. I'd like to cut cable and switch to Sling. I still think I have more to do to convince her of the math behind early retirement. But these will all take time.
Also of note: we too are planning a wedding. We went to the library together and got two books: one on wedding planning must-do's, and another on saving money for the wedding. That gave her HER OWN ideas about how to save for the wedding, which she is implementing. I expect it to cost maybe $12,000, which will be offset by the $10,000 we are getting from our families as well. It has made the planning process a lot less stressful.
Now, I know that's probably a boring and non-dramatic post, and I can certainly say that the library wasn't the magical answer to all our money issues (there have been many hours of money discussions...it took almost a year to get her to increase her 401k). But I think the biggest thing I have done thus far is not jump straight into the deep end. Starting with "I want to retire in my 30s, you need to switch A, B, C, and D, and stop doing E" is insane if your partner doesn't understand the difference between a traditional and roth IRA. I think you absolutely need to build the foundation of personal finance before getting into anything more nuanced, especially a goal as novel as FIRE.
I say that because it seems like you've immediately jumped to FIRE and skipped the basic steps. You're taking your own personal finance knowledge for granted. I'd bet your fiance has a decent head on her shoulders, and you're basically screaming "YOU'RE DOING IT ALL WRONG." That isn't going to fly because, naturally, she is going to feel attacked.
I'll also add: I bet you also didn't get into FIRE overnight. You probably looked at other personal finance blogs, read other personal finance books, etc. before finding MMM. But now you're expecting her to jump straight to MMM?
Sorry, but that's not fair to her. I think you need to look in the mirror and understand where she is coming from. Instead of criticizing her a half a dozen times about not understanding "simple" compound interest (again, you're taking your personal finance knowledge for granted), why not go to Barnes and Noble and buy a few books together? "Hey babe, since we are getting married soon, I think we need to work on our understanding of money. You want to grab a few books? I heard X, Y, and Z were good starter books for young couples." THEN LET HER FIGURE IT OUT.
Like you, she will see the light. She will be six chapters into a really good book from an author she respects, read about how fees impact her returns, and she will sprint to her computer to switch her funds. She will see how increasing contributions from 10% to 20% means she can retire 5 years earlier. A light will click, just like it presumably has for you.
All in all, this is just a long post with my anecdotal example that reiterates what others have said: this isn't about money, it's about communication. I'll disagree with others, though: you don't need to break up over this. Work on it. Your fiance presumably has a ton of great qualities. Think about why you got on your knee and asked her to marry you. Then work on your communication skills. Best of luck to you.