He didn't want to be a nanny. He wanted to be back in the family home after his wife ends their marriage. He dressed up a woman (with an elaborate latex special effects mask) to fool his wife into hiring him as a nanny for their children. Partially to spend time with his kids, but mainly so he can convince her to go back to her husband and break up her new relationship with Pierce Brosnan.
It was adapted from the book Madame Doubtfire by Anne Fine, which was much funnier, but also more unrealistic in that the wife and oldest daughter don't immediately recognise their husband/father who isn't even wearing a latex mask in the book. What is good about both the book and film is that by the end Daniel recognises that he was a shit husband and father and accepts that his wife made the right decision, they go on to have an amicable divorce and he makes a better effort as a father.
I'm thinking that the main reason there is an attempt to cancel the film is the scene in which the two older children realise Mrs Doubtfire is a man. (This scene isn't in the book.) They walk in on him standing up to piss and immediately freak out, assuming he is a threat and a predator. IIRC, the boy is afraid and grabs a tennis racket to protect him and his sister. And they are only calmed down upon realising the man is their father. It re-enforces the idea that random men dressing up as women to access the private spaces of women and children is something to be justifiably scared of.