What would happen if a LED tube on one side of a fluorescent fixture, and a regular fluorescent tube on the other side of the fixture. Would the ballast burn up, or stay normal?

Been curious of this myself...

If they're parallel wired I'm going to guess it doesn't matter. Wiser folks than me will know for sure.

I've used a fluorescent lamp and LED retrofit in series for a short time and saw no issues.  As long as both lamps are intended for use with the given ballast, I'd expect it to be fine.

One potential problem i see - in ballasts where the 2 cathodes on the Yellow wires are in series, the FL cathode could possibly not be getting its heating supply and starting/running cold. In ballasts where the cathodes are parallel it would probably be ok

Surely if its a switch start fitting the starting pulse would kill the LEDs if they were on the same ballastt

I have done this with PL led retrofits when one of the leds does fail i put in a fluorescent 42w 4pin, ballasts run lamps in series and the led even glows while the fluorescent preheats,a lot of times the led PL will not light at EOL but the series lamp works fine. anyways this works lomg term with no issues! On a parallel ballast it may mess it up since it's not running same wattage on all outputs