I am not diagnosed with autism, I am still going through an assessment, and have my interview portion coming up in two days. I highly suspect that I am autistic however (most of the time, but have pretty huge imposter syndrome at the same time).

Personal hygiene is hard for me, and it is really embarrassing for me to say, and I would never say this in front of most people. Showering is a chore. I don't like being wet, I don't like the different temperature zones that are created. I don't like the noise of the fan, and the shower head. I don't like scented body washes and shampoo. I don't like scratchy towels on my skin or how long it takes to get dried off. I don't like the sound or feeling of a toothbrush. I hate the smell of deodorant. Maybe your partner is also having sensory issues that make personal hygiene hard for them?

I am not excusing their behaviour, and I think you absolutely can ask them to take better care of them self. You already have great advice from u/QBee23 in regards to how to go about communicating with them on this matter. So I will just stick to coming up with other ideas.

There are many things that I have read about on here, and in other autism subs that people do to make personal hygiene easier for themselves, you could use the search function and I'm sure you'll find many more ideas than I can think of. But, do you know specifically what it is about showering and tooth brushing that your partner has issues with? I find the best solutions come from fully understanding the root cause of the problem.

I could suggest water proof headphones to drown out the noise from the fan and shower head, but maybe noise isn't the issue. Maybe it's more being cold and wet when they get out of the shower in which case maybe a space heater, or a heated towel rack might be the answer. Maybe they don't like using a scratchy towel to dry their body so instead they might need a nice big soft fluffy bathrobe and a pair of fuzzy slippers to put on after wards to wear around the house until they are dry. Maybe they just never really think about doing it, and just plan forget in which case a daily planner, app, calendar, or note on the bathroom mirror etc could help.

Anyway, good luck with finding a solution for you and your partner. I hope you can come to a compromise. And if not, it's ok too! Sometimes people are just incompatible and it doesn't make either person 'bad' for not being able to accommodate the other for whatever reason.