Not sure if my experience helps, but as you asked...
We had significant hygiene problems when my mother first moved into very sheltered accommodation and problems with her clothes not getting washed are starting to reemerge.
Initially it was hugely important that we conquered it. My mother pre-dementia, would have been horrified at herself. She became very disorientated from a UTI and had just invested £200,000 in her new flat. Somehow between hospital and convalescent care she had lost a lot of her routines. Everyone wanted her to to get back to a point where she could manage semi-independent living.
The various helplines were not helpful. You cant make someone do something, only prompt. (The CH she was in for convalescence however seemed able to ensure she had a thorough wash.) I, and to some extent the carers, were blunt. (Me blunt?? I think my latest post on the longer thread suggests I can be.) She had to wash herself and have her clothes washed or she was back in the Care Home.
She loves where she is and somehow the message that she has to be on her best behaviour otherwise she could be out, seems to have persisted. Not necessarily a bad thing as it helps her focus on social presentation, despite the huge disability her memory loss presents.
What really got to her was me coming in and first thing checking the laundry basket to see if yesterday's clothes were in there. Its a bit like catching a toddler who has denied wetting himself. The carer did the same. My poor mother really hated it, but there was a result until her primary carer went on maternity leave and I had assumed the habit was sufficiently ingrained. The current carer is starting again, and seems willing to put up with the abuse and moaning. Otherwise I had planned to go down and go through her drawers and pull out everything that had a remote whiff, eg anything she wore regularly, and run it all through my washing machine.
My mother agreed to this last week, again because she does not want her current accommodation to know how much she is struggling. (They know of course - but I suspect that if she were unable to keep herself clean, and therefore healthy they might say she would be better off in a setting where hygiene could be imposed.) She will have forgotten, but deep down and based on conversations we have had since about the assertive approach I took at the start of the year, I know she, or at least the un-demented she, understands.
I would have a very frank conversation about the consequences of not washing. If your MiL cant comply she will end up going down hill quickly, especially if she catches a winter bug, and wont be able to stay in her own home. You want to facilitate her staying where she is. The carers will be instructed that their first priorities will be heat, food, medication and then hygiene.
You could then discuss with them, and especially the lead carer, how to go about this. Be careful to recognise and support the efforts and achievements of the lead carer. Its hard enough imposing something on a relative, but a carer who is willing to push preventative measures despite having to endure abuse etc. I also reckon that a "spring clean" of all clothes twice a year would go a long way. Easier for me because I have already moved my mum out of her original home and so though I prefer to respect her privacy, she is more used to me "interfering". The carers could also note in the care book what she is wearing each day, so different carers can keep an eye on whether she is changing her clothes and whether dirty clothes go back inot the drawer or into the laundry basket.
And as a final PS to a long post, I am enjoying the clash between a generation who saw a bath once a week as sufficient and who grew up without washing machines so dont see the need to wash outer garments very often, and a young carer who seems to believe that everything should be washed after wearing. In fairness the sheltered accommodation is far warmer than my parents home ever used to be. I remember gong for Sunday lunch and cursing the fact that I had forgotten to wear a wooly jumper and thick tights. I think they are reaching a compromise, but not without a good debate. A good reminder that I need to buy the carer a Christmas present. I don't think she is on my mums gift list, though oddly in the longer term I think she prefers carers with character.