That is a very naive view of the left. Yes, they may claim to support the things you mentioned and even have partial success at achieving them, but that is only half the story. The left constantly needs new causes to justify its existence, new enemies to fight. The most blatant inequalities in the west have already been solved, so the left begins to abandon its old causes (workers' rights) in favor of increasingly more abstract ones, such as social justice, where they can endlessly fabricate new problems to solve. In some cases, they'll shit on the people they claim to fight for, such as when promoting mass third world immigration, leading to worse living conditions for lower classes, in addition to the lowering of wages for low-paying jobs due to the introduction of unskilled immigrants into the workforce. So now you've divided the lower class, giving you new "injustices" to fight while simultaneously gaining new voters who rely on gibsmedats. Add to that the promotion of anti-racism and diversity and the modern left's condescending attitude towards native blue collar workers and it is no wonder that we get results like last year's general election in the UK where Labour took a hit.

For it to survive and have any real value in today's West, the left needs to be reconstructed, stripped of its Marxist elements and harnessed to solving the core issues that resonate with ordinary people and their daily lives. Remove the champagne socialists from their positions of power and purge the ideological elements of leftism (if even possible) and I may yet respect it one day. As it is, the left is a self-contradicting, bloated, ideological mess with little connection to reality.

I consider myself a conservative and I do care for equality, much like the left, but my means of attaining that equality are pragmatic. You can't have your cake and eat it too - you must set limitations, you must exclude people, otherwise you're just fighting windmillls. If you care about gay rights, don't import people who are statistically very likely to hate gays. If your cause is anti-racism, don't push for 'diversity' and shit on whites for caring for their own people, you're just going to create resentment, intolerance and traction between people who might've otherwise gotten along.