The way to push them left is to actually push them left—protesting, calling your representatives, donating to campaigns you support, voting for candidates in local primaries where your vote is exponentially more influential, et cetera.

But voting in a presidential election doesn’t push anyone anywhere. For one thing, pushing is a continuous, incremental feedback process, while the outcome of a presidential election is a discrete binary one—there’s no map between the two. But more significantly, this buys into a narrative that the media has constructed over the past few generations, in which voting is a semiotic process with the people signaling their desires with their votes and politicians signaling their response with legislation. This leaves the media in full control of the political process by interpreting for each side what the other “means”: because the votes and bills in themselves are devoid of meaning beyond their real effects, the media is free to insert whatever meaning suits them.

Why do you care if the person you voted for wins?

Because it's an election with consequences, not an online fandom.

Voting for a third party, like trying to walk through a third door, is an indication of intent. Going through the door would be getting them elected to office.

And yes, supporting a party would be endorsing whatever evil policies the party supports—but voting isn’t an act of endorsement. Nobody knows how you vote; it has no meaning as a personal statement. Its only meaning is in the differential effects of the policies of the two candidates your vote decides between, in the most likely scenario in which it is the deciding vote.

You absolutely should support and endorse a party you believe in, but don’t mistake voting in a presidential election for either of those things.