Fast fashion - it depends on how much gets thrown away at the end of the day? Just because clothing has a heavy toll on the environment, doesn't mean companies producing it are evil. Toll on the environment or not, people need clothes.
It sounds like you are taking this for granted and something that can't be changed. In fact there are a lot of initiatives and companies that work on reducing the footprint, using sustainable sources of cotton, paying fair wages, using less harmful dying methods and filtering the water used in production. If you are interested in the topic I'd suggest to start with https://en.wikipedia.org/wiki/Sustainable_fashion.
As for the green washing, there are probably better sources ([1], [2]) for that but you'll find enough if you do a little research yourself.
[1] https://ecowarriorprincess.net/2018/08/can-hm-ever-be-sustai...
[2] https://wellmadeclothes.com/articles/HMConsciousCollectionIs...
In any case, if you decide on that logic, everybody who shops at HM is evil, too.
At very basic level: have these "sustainable fashion" people figured out a way to grow cotton with less energy and less pollution? If not, they don't really have a solution for anything. If they have, they will probably prevail on the market anyway, without the "fair" marketing.
And the use of "fair" usually just implies that some people want to make the rules. I honestly don't care for that label, at least when it is used in marketing. In my opinion fair prices can only be determined by markets (with externalizations being paid for via laws).