I am trying to replace a four-way switch. There are two cables of four wires each coming into the box, but the red wires are connected with a wire nut, rather than the white wires. The house was built in 1976 - it may be the original wiring.

What gives? I'm not sure if I should change it so the white wires are connected with a wire nut, and the red wires go to the switch, or just leave it the way it is.

I would put black tape on any wire that will be live(whites going to the switch)and Leave as it is.

I agree with Strat, replace the switch and leave other things alone.

It appears that you think that because a wire is white it is a neutral. In this wiring it is not. The white and black are both travelers between the switches. The red wire is the path for the current to return from the load (second) 3-way switch to the box of the line (first) 3-way and from there to the light.

Perhaps you should tell us why you are replacing the 4-way switch. Switches do fail but it is unusual.