Also, Uber and Lyft began and are headquartered in literally the most leftist city in the country, San Francisco. The notion that "leftists" don't want Lyft or Uber seems odd.
"The left" is a broad group with many different ideologies. I don't think ride share companies that flaunting regulations to even be a left vs right issue. It's more entrenched encumbent/rule of law vs anti-regulation/technocracy which doesn't fall into any neat categories.
San Francisco has attracted many sects of contrarians over the years. It is like a leftist museum.
While leftists have all kinds of diverging attitudes, there definitely is a large population who don't want Lyft or Uber -- especially Uber. When companies reach a certain scale, no matter how liberal they are, there are large portions of the left that push to see them taxed or hemmed in somehow, because deep in the leftist world view is a sense that something unfair has happened. Part of this is due to the contrarian ethic, that rejects playing by society's rules; and part of it is due to communism's lasting influence. Entrepreneurs enjoy only tenuous legitimacy, and inevitably lose it when their company proves to be just like all the others.