Massive debt that can't realistically be repaid would probably be an issue, at least I'd need to research laws and stuff to know how it would affect me to marry someone in those circumstances.
Beyond that, the amount of debt isn't nearly as much of an issue as the attitude the person has towards it and towards money management in general. If they take the responsibility to pay it seriously and have established and are sticking to a plan to make that happen and get out of debt; it's not going to be an immediate disqualification. But if they have an attitude of only doing the minimum required and blaming other people for their being in debt, well that's probably the attitude they'll take towards their marriage commitment and marriage problems, and because of that fact, I'm bailing on them. At least as far as anything that could lead to marriage is concerned.
And at the moment at least, I can be added to that collection of rarities that are debt free women. But I would consider going into debt to buy a house or car if necessary. And I use my credit card for most everyday purchases, but I always pay it off every month. As far as establishing good credit is concerned, if you never intend to borrow money then credit probably doesn't matter too much, but the way I was raised I go with better to have it and not need it than need it and not have it (assuming you can manage your credit and money well enough to not be losing a lot of money to interest charges).
And I think, though I'm not positive, that the way credit is reported, having a credit card is what counts. Even if you leave it in your dresser drawer and never use it ,you still are reported as paying your credit card bills as agreed and building credit. But having seen too many people in money trouble, I'd say if you can't manage your money well now, don't even think about getting a credit card. Too easy to end up paying massive amounts of interest.