Is it important to have a schedule for going to bed and getting up for a 90 year old mother with Alzheimer's?

Yeah, whatever works for the caregiver and keeps the LO healthy, would be my goal. People who have dementia, often sleep more and more as they progress. If it's working, then, what would be the downside?

If she is living with sis, let sis makes the rule unless mom's health is CLEARLY impacted.

My 96 year old mother is in assisted living with advanced dementia. She was always independent and sometimes doesn't want to be woken up. I think it depends on the person. If your sister is caring for her, you may want to let your sister decide on that one, as she is bearing most of the burden. There are ways to change diapers in bed and even clean people. They must be "turned" if they are lying in bed for long periods of time so they don't develop bed sores. If your mother is in hospice, you should make her comfortable. My mother likes to sit up in a wheel chair (she can no longer walk on her own) in a room with other people.

I think that in general people do best with consistent routines. Although none of these may apply in your mother's case some concerns I would have are:
medication schedule
continence/toileting
sleeping later in the day leading to being awake more at night
too much time in bed leading to decreased muscle tone - use it or lose it

What time is she going to bed?
If she goes to bed at 8 pm and stays in bed until noon 15 or 16 hours in bed without being changed is a long time. Unless mom is being changed during the night.
My Husband was pretty much on a schedule in bed by 7 (that was his doing at the start.) and I would get him up around 7 am and into the shower. He would sleep during the day in his recliner early on then in his wheelchair. But we would waken him for lunch and dinner and to change his briefs. (pull up then later tab briefs) All total he would sleep on average 12 hours a day and that progressed to sleeping about 20 to 22 hours a day as he declined.

A schedule is good for the caregiver for several reasons, the caregiver can get tasks done, plan when a visit from a friend might be possible.

The longer she sleeps in the day time, the later she will want to go to bed at night. The last thing you/your sister needs is to wear out from your own lack of sleep...and... it's going to happen.
It is easy to let them sleep while you get things done around the house, but you are creating a 24 hour active caretaking job.

The person caregiving the most should be the one deciding. No doubt a relief to know those hours will be some she won't have to be watching mom. If she's in bed she's safe and not getting into mischief. Let it go:-) And such rigidity at the assisted living! I'd never put up with that nonsense...paying money and people telling ME when to get up? No way. Especially at that hour.

I’m inclined to support whatever works for the household they are in. Just like raising kids, you will have to weigh your own needs In in order to manage.
A facility has MANY concerns, so scheduled time would be very important to maintain each need of all residents.

In my honest opinion, your sister should decide since your mother is living with her. Perhaps she and you should be concerned about sister's sleep schedule since she is the carer.

Actually, I can see why sister allows her sleep. I think the hours of sleep quoted is for someone not suffering fromba form of Dementia.

"They tend to get less deep or 'slow-wave' sleep, which helps to keep the brain healthy and refreshed. Even though a person with dementia may end up sleeping more than a typical person of their age – even as much as 14–15 hours a day – it is unlikely to all be good quality sleep.Mar 21, 2019"

Here is an article

https://www.sleepfoundation.org/articles/alzheimers-disease-and-sleep