If you're with someone you can see yourself marrying, and there are things about them that you don't agree with, do you...
Marry them anyway, hoping they'll just change in time and that things work out?
OR
See that as a red flag and realize that you can't marry someone in faith, you gotta see fruit/evidence now?
Its a very tricky situation, one that you really need to not only have a very serious conversation with your partner about, but also alot of soul searching.
It also depends on what exactly you're talking about.
First off, you'll need to stop thinking about even the SLIGHTEST possibility that the other person will change. When you contemplate these differences or issues, you really need to ask yourself: "Do I WANT to deal with that for the REST OF MY LIFE?" Not "CAN I deal with it", because its easy to say "yes" to that. Look at the situation with as much logic and lack of emotion as possible. If you realize that, no, you do not WANT to deal with that forever, then you have two options: 1) discuss it with your partner in hopes that a solution can be made. 2) don't marry them.
You'll need to figure out how these differences will affect your future and everyday life. What impact will it have on raising children? On your every day and long term happiness and well being? Next to finances, religious/moral differences are at the top in terms of what leads to anger, resentment and divorce.
From experience, I almost married someone who just wasn't right for me. Yeah, I loved her to death, but there was a LOT of emotional baggage and moral...looseness, shall we say, and I did everything BUT what I'm telling you to do. I tried to ignore it. I tried to show her the "correct path". I asked her to marry me because A) despite those flaws I thought i wanted to be with her and B) I hoped that she would see marriage in a more serious light, and someday she would change. I was wrong on all accounts and was forced to learn the hard way what I and others are telling you now.
If there is anything you need to over think and take your time until there is no doubt, marriage is it. Be 100% open with your partner about what you're thinking. Don't expect them to change, don't try to force them to and CERTAINLY don't compromise your own beliefs and morals to make things well, because quite frankly, whatever serenity you might find with that route, it will be hollow and short lived.
Good luck.