Are the passenger seat belts pulled all the way out and won't retract, or are they stuck in the retracted posititon?

If stuck all the way out and won't retract you might be able to access the retractor to find that the pendulum is wedged in a cog but the belt is out so far that you cannot pull it enough to unseat the pendulum from the cog. If you were to pull the belt out has hard as you can, then have someone release the pendulum from the cog the seatbelt may one again function properly. I've had this happen on two separate Fords of similar vintage to your Explorer. The first was in my first car, a 1988 Escort EXP. The belt was that way when I bought it in 1990, I did the above and it never acted up again for the 9 years I owned it. The second time was in a 1993 Taurus SHO which happened while I owned it but only the one time.

-Rod