First of all, what are you trying to acccomplish? Are you trying to get the monitor to tilt one direction, then the other, to allow players a better view? Either way, the orientation would stay the same.
Magnetic interference can be caused by moving the monitor - period. It doesn't always happen. You are more likely to have it happen on an older monitor than a newer monitor. If you are using a computer monitor, it may never happen. Older G07's are the biggest culprits of this, I've found.
Some monitors have their own degauss buttons installed, and it's quite simple to wire it up to an external button for degaussing if needed after tilting.
Certain cocktails like Centipede had a small tilt motion built in. The entire cab would tilt while the legs stayed still. This is probably the best way, as all the electrical and electronic parts inside move together and remain the same distance from the yoke throughout. Tilting the monitor alone will cause the yoke to move closer, then farther from internal components, increasing the chances of interference.
Hell, just go read the post in "Main" on how to build a Joust cocktail cab, with both players on the same side and the screen tilted a bit automatically. Be much easier.....