Replacing Ceiling Fan/Light with light only wiring mystery
When someone does a light fixture replacement with switches involved and has a problem, it is usually because they reconnected the white wire that feeds power to a switch back to the other whites thinking it is a neutral.

Then they connect the black to the hot feed throw the switch and it trips the breaker because it is now a dead short. 

When using cable to feed switches and return a switch leg, the proper practice is to feed the white wire hot to the switch and return the black wire to the light from the switch. Then (and this is the part many people don't do) you are supposed to re-identify the white wire as some other color. Black tape or red paint or something permanent. I like to use blue tape since you don't see blue in residential wiring. This show the next person that this wire is a switch feed NOT a neutral.

Sounds like the red is a hot feed from the panel that powers the whole circuit. If you are testing for "hot" with a no-contact tester you can get false positives that are from induced currents. You need a basic electrician's voltage tester. 

You may have to take all the wiring apart and methodically identify each cable and conductor. Then plan how to reconnect the wiring to accomplish your goal.

Good luck!