New Bathroom Light Fixture Issue
"Hooking it up normally (black to black, white to white), the light fixture will stay on when the power is turned on at the breaker and the switch does not turn it off."

This tells you the black wires under the same wire nut and the white wires under the same wire nut, are the hot feed wires from the main panel. This is as it should be. The white wire from the fixture should go under the wire nut with the other white wires. It should never be connected to a black or red wire in normal configurations. (The configuration you have in the picture is incorrect as you have the neutral for the light connected to both switch legs under the same wire nut.)

If there is only one three-wire cable running to the switches, then the white wire should be permanently re-identified as black and it will be connected to the hot black wires in the J-box and become your hot feed to the switches. This is the proper way according to the Code. Then the black wire and the red wire coming back from the switches are your two switched legs. For example, black for light, red for fan/light.

Good luck and stay safe!