Surge protection not working on a home projector
The problem is not surges, but rather dips in voltage caused by the other loads. A surge protector or an UPS will do nothing for those. Except, of course, if the dip is low enough to convince the UPS that power has failed, in which case, it will start up.

It seems that your projector is particularly sensitive to these dips, and it's going through a reset/startup sequence when they occur. Normally, the filter capacitors inside its power supply would contain enough energy to "ride through" short dropouts and dips. It's possible that the capacitors in yours have aged to the point where their capacity is severely reduced.

The fix would be to replace the capacitors &mdash; or the entire power supply, if it is a module. The alternative would be to get an AC voltage regulator, but these are not cheap.