Rinsing them is absolutely fine. The "food science" recommendation around cooking mushrooms has changed in the last few years. Many cooks are seeing good results by starting to sautee the mushrooms in water and only cooking with oil once the water has boiled off. This enables the air pockets to collapse and for a lot of the moisture to evaporate so you end up needing significantly less fats. I've switched to this method myself, and I've been very happy with the results.
https://www.americastestkitchen.com/cooksillustrated/article...
https://www.youtube.com/watch?v=OPJmJdStvwI