I applied sealer to Mexican tile and within a few hours, it rained.The finish on the tiles now is cloudy. Will this clear with time as everything dries or should I bake the tiles to burn off the water trapped in the sealer?
Unfortunately the cloudiness will not likely go away. The problem is that there is moisture in the sealer and the top of the sealer is not smooth. You may be able to fix this by just polishing the tiles with some steel wool (not the kitchen kind, the 00 or 000 polishing kind). Basically, just use the steel wool like sandpaper and rub out the finish. Rubbing out your finish is something that most woodworkers do to get a smooth and clear finish on their work and it also works for any other type of finish. If the steel wool doesn't work then you will want to either sand off the finish or use a finish remover to get the finish out. If you bake the tiles to burn off the water then you will likely yellow the finish or, depending on the finishing product, burn and blacken the finish.
The cloudiness you see is called blushing--the remedy will depend on the finish that you used. If it a lacquer you can use blush eliminator, I have never tried it on shellac or enamel. It may go away after it is dry however. Sometimes the moisture in the air will cause the finish to blush.