I can empathize with the notion that voting for a third party is "throwing your vote away", but it's really dumb to say it's like voting for the other party. No it isn't.
I remember a Facebook argument I had about the Quebec election of 2014 in which people were saying "liberals got elected because of non-voters". To which I answered the obvious: " Actually, liberals got elected because of liberal voters." They didn't appreciate.
I disagree whole heartly and mathematically.
In a first past the post voting system, with a finite number of votes: casting a vote for someone is just as much a +1 as it is a -1 to the opposition; while not voting at all is 0 for both.
If you have two people to chose from, that doesn't matter. It works as basic logic tells you it does.
Now consider a ballot with three names - ding dong - you know have a king maker in the system. In this case it's Jill Stein. Jill Stein is effectively the nominee of the people who would vote for Hillary if they were to vote otherwise and her name wasn't there.
Given the dichotomy politics of the US what you have is a system of two parallel elections:
BURN IT ALL(Trump) vs SRS PPL(Clinton) and SRS PPL vs Fuck_Clinton(Kingmaker)
Ultimately, you have two elections going at the same time.
Not voting gives you a zero throughout the board.
Voting for trump gives it:
+1 to BURN IT ALL and -1 to SRS PPL and 0 to Fuck_Clinton, because the Kingmaker isn't competing with Trump.
Voting for Clinton gives it a:
-1 to BURN IT ALL, and +1 to SRS PPL, and -1 to Fuck_Clinton.
Voting for the Kingmaker gives you:
0 to BURN IT ALL, -1 to SRS PPL, and +1 to Fuck_Clinton.
Voting for Jill Stein does not affect Trump, as they aren't competing, but to Hillary it's the same as voting for Trump. So ultimately it's 1/2 as effective as voting for Trump would be.
Voting for Jill Stein would be the same as just throwing out your vote only if you would never under any circumstance vote for Hilary(Or Trump). In that case yes, your vote is irrelevant no matter what you do. However if you just like Stein more than candidate X, then it is not, it is voting for the opposition of candidate x.
The first past the post system only works if you have two candidates. The only other way for it to work if you have more than two candidates is if every candidate is in a position of dichotomy against EVERY other candidate. If you have more candidates and they overlap with primary two most popular candidates - they become kingmakers.