Cisgenger woman, so please ignore me if this isn't welcome, but I would love to help!
I wash all my bras in the machine, on cold and hang them dry. Putting into a lingerie bag is a personal preference. (I only do it if I'm washing other stuff with zippers) If there are deodorant stains, vinegar is pretty effective. Soak the bra and use either a toothbrush or (I know this sounds crazy) the foam top of a dry-cleaner coat hanger, to scrub off deodorant. Idk why the coat hanger foam works but it's great!
Yeah I'm trans but I transitioned a decade ago and young enough for my mom to teach me how to girl (ok I was an angsty tomboyish lesbian at the time so I brushed a lot of it off but I did learn to wash a bra)
And yeah, I used to hand wash and if it's got hooks or anything delicate it gets hand washed in the sink and hang dried in the shower. Otherwise it joins literally everything else in the washing machine on cold and delicate and thrown in the dryer.
Has this influenced which bras I buy? Yes. I've definitely developed a high effort high femme style, but that's for high effort time. I'm not putting in that much effort for a bra that's job is literally just to make me professionally presentable at the factory. Which really is proof I'm my mother's daughter.
Mine only connect if there's a lot of lacey/delicate things in the wash with them. If you hook them together before they go in, they're less likely to come apart, but once I started throwing them in with shirts, sweaters, pants and PJs, they stopped hooking into other things.
Idk why the coat hanger foam works but it’s great!
A wild guess, but I wonder if it's melamine foam? We use blocks of the stuff here to clean all sorts of things around the house. Works great on metal, too!
I also have bra washing suggestions! (I have some executive function issues, so I try to share my tips.)
My partner does what you do, because she doesn't wear any underthings with foam or wires and she hasn't found that method wears them out.
I used to put my bras in the washing machine, but the underwire would always cause some sort of issue. (I also love my underwire bras... They keep everything in place better than without.)
I have this little dish tub I put mine in, and I clean using this soap called "Soak." No scrubbing, I just dump it in there, swirl a little and wait like 15 minutes. I then squeeze out the water (gently!) and hang to dry. It's super easy and helped me keep everything clean and in good condition.
I Iike bras hanging on the side of the laundry bag so I don't dump them in the machine right away like the rest of the clothes. Do the same with anything else that needs mesh bag. I'm not sorting laundry!
Mesh bag makes it easier for me to find what doesn't go in dryer too.