The water exiting the washer is fully occupying the drain line. Passage of the water displaces (pushes) air in front of the flow, and creates a slight vacuum behind it. If the vent stack serving that line is insufficient (too narrow), occluded or missing, the vacuum created in the line impacts other lines that are connected to it.
If this is a sudden occurence, your vent stack was recently impacted. If it has been happening since forever, your stack is insufficient or absent. Check for the presence of and blockages in your vent stack. Get a plumbers snake and a flashlight and climb on the roof. Look down the stack to see if a blockage is visible. Snake to remove, or just generally snake the shit out of it for as far as your snake can reach. Bring a couple gallons of water with you to help flush the blockage further down into a larger pipe.
Caution: Keep a firm grasp on your snake - or tape a big wad of rags on the end so it doesn't inadvertently all slide down the drain. Neighbor did this years ago, and had to call out the pros to retrieve it.
Thanks for the detailed response, it makes sense. I already scoped the sewer line, but hadnt thought to check the vent. I'll dig my scope out and check it. This has been going on for years and I only caught on to why the toilet bowl would "randomly" be bone dry through dumb luck of walking into the laundry room while the washer was draining.
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