Where did you get all that ridiculous bullshit about Yellow Vests protesting for social inequality, climate action, ecology, "communiques", and other quasi-communist leftist cant.
They have been protesting because (a) they're French, hence masters of protests, and (b) because their government supports all the shit you mentioned in your post and generally sucks.
Yellow Vests is the OPPOSITE of the ridiculous shit you posted. However there's no doubt that leftist scum are trying to co-opt the movement.
How do I know this? Because more recently people are showing up to the protests wearing funny hats (no pink pussy hats spotted yet) and clown noses, both sure signs of leftist infection.