Is posting me exercising with my own dementia mother happily offend my mum’s dignity? Or the sibling’s own toxic seeing the decline mother.

Your mom is part of your life and there's nothing wrong with sharing your life on social media, within reason, and it's certainly abused and done inappropriately by people all the time. You shouldn't have to hide a fun activity you and your mom enjoyed together. It's not a picture of her naked in a bubble bath for goodness sakes. Everyone's relationship with Facebook is different, for a lot of different but equally worthwhile reasons. If you honestly believe she would be fine with your "friends" seeing the picture then you know best. If your sibling is having some sort of freak out it's worth exploring their feelings too. There isn't a right answer, you have to really do what you believe is best.

Interesting question. I consider myself outgoing but I do not like being the center of attention. So for me, I would not appreciate something like this posted. I didn't even have a profile picture on my Facebook acct at one time. A friend posted one I liked so that is up there now. But that's at least 5 yrs old.

My grandson has a picture of my Mom on his FB page. It was taken in the NH. She looks so old and frail. I know she would hate that picture but he was so glad he got a picture of her before she passed.

You know, count me first of all, OLD> I will be 80 this year. But were I your Mom I would not want this private activity that, YES, WOULD be fun for me were I to do it with my 60 year old daughter, posted out to the world. I think we "share" too much with a social media. On the other hand, you are doing no harm if your Mom LIKES to see herself filmed and presented before the world; perhaps she feels like a "star". I think this is a private decision of your own, as you know your Mom. For myself, if I saw my Mom, who is incapable of now a rational decision, on screen posted to the world it would make me want to curl up in embarrassment. But, as I said I am a private individual, and of an age. I wouldn't want to be seen in my swinsuit either at this point, unless in the privacy of my own home.
Who in the family or outside it is upset with you, if I may make so bold to ask?
Wishing you the best, and in all of this, thrilled that you and Mom can have some fun together......that in the end is the point.

Your mother is not competent to consent to you posting her image on social media, so yes, you're out of line and violating her privacy.

Just use common sense. Posting video of her on social media serves no real purpose, so just stick to posting your own stuff without involving her.

Your sibling is not "toxic;" they're 100% correct.

I do think there is a trend to over share on social media. In order to judge whether or not something is appropriate you should ask yourself if this is something your mother would have been OK with pre dementia, if she was a very private person it may not be. It also depends on how wide an audience you are sharing with, I would advise posts like this are limited to close friends and family.