While being a very mild Aspie, I do like some routines. And I do feel slightly distressed if they are changed, but it's not hard to cope with.
I get ready for work almost exactly the same way every morning. I change my routine a little bit based on new things I have to do / old things I don't need to do anymore. But generally I figure out what works for my needs, and then optimize my routine to death, and then stick with it as long as I can until something changes. I shave the same way and always shave first before anything else. And shower the same way going through all the same motions, and dry off the same way, dress the same way, etc. etc.
I always set up my laptop the same way every morning and do the same thing with my phone and coat, and I have consistent routines for getting home and going to sleep too. I change out of my business casual stuff and into street clothes, and all the stuff in my pockets and my work laptop get put in exactly the same place every day.
I notice things like hating to leave my closet door open for any reason, and feeling satisfied about keeping a consistent vitamin regimen. For lunch, when a new place to eat out opens up, I tend to go to it like 50 times in a row; then I can't stand it for a while, then it gets added back in with the other places to eat for variety.
There are variations on all these things, and I'm a lot more flexible during the rest of the day, but all these little "getting ready" routines are my anchor.