What is the best way to clean your running shoes? Should you wash them in the washing machine or will that break them down too much?
You can throw them in the washer (with a good shot of bleach to kill off everything). Remove the insoles, and throw them in too. It won’t seriously damage the shoes, but will shorten the life a small amount (it puts a bit of wear on the upper fabric, only an issue if you keep shoes for years vs. wearing them out every several months).
A couple of tips:
Air dry them, heat from the dryer will damage the glue.
Put an old tennis ball in each heel. This helps the heel counter keep its shape while wet and going through the spin cycle (this is not an issue with plastic heel counters, but many brands cut corners and use “chemical sheet” which is treated cardboard).