My MIL is at the point where she doesn’t want to take a shower and can’t by herself. She is crying etc at her facility when they ask her to.

Maybe a hand held shower will help if she holds it. My Luz loved using the hand held in our step in tub. Before that she used a small container to pour the water over herself and loved that as well.
A sponge bath and a small tub of water for her to sponge over herself might lessen the trauma of water pelting her skin.

This is a common thing LOs do who have dementia. I would request a same-gender aid to coax her to shower. Can she have a sit-in bath instead? Maybe a sponge bath to get by? Depending on her level of dementia, you can maybe set up a "date" with her but prerequisite is she needs to shower to go with you. Just trying to be creative here :-) We eventually ran out of ideas for my 97-yr old auntie with dementia and it was one more thing to exhaust her sister caregiver. She eventually hired a neighbor for $30 per shower to come in once a week. This women happened to already work at a facility and knew how to gently coax her. A great solution so far, but I realize your MIL is already in a facility. The facility can't force her to do anything, but the admin might have other ideas if you ask them rather than staff.

Oh dear, I wonder if she is afraid of falling in the shower or embarrassed to have an aid help her. They make capes for keeping one covered after the clothes are removed. Maybe something like that might help her. If she can have the same aide for bathing she might get comfortable after a few sessions in the shower. Just brainstorming what might keep her from wanting to shower. I’m assuming there are grab bars etc for her in the shower.