First thing to try is to add a mains filter to your speakers' power supply. Something like this:
https://elektrodump.nl/nl/lichtnetfilters/2442-lichtnet-rfi-filter-4a-250vac.htmlThis one is meant to build into a device. There are smaller ones too, just make sure they at least have a capacitor-coil-capacitor layout.
Make sure to hook the filter up to a grounded outlet, and if your speakers have it, to connect their ground too.
This will suppress the RF pulses that the various inductive loads create.
Before the filter, you want to put a surge protector. This is to short out any high voltage spikes that may be present on your mains, to extend the life time of the filter. They don't last forever.
I'm assuming active speakers with built in amplifiers here, not standard speakers with a separate amplifier.
In general, if literally all lights and the fridge do it, the issue is your speakers being too sensitive. But it's a fact of life that glowbottle starters and inductive ballasts puke out a ton of spikes and RF when starting. That's why many countries have strict RFI rules. If you have a ham radio operator nearby, you can ask them for help - they typically have a lot of experience with RFI suppression.
You also want to verify that the suppression capacitors in your lamps' starters are still in good condition, or that they're even just there.