No, it is not a wasted vote for many reasons:
1. It Influences the Major Parties
It lets politicians and political parties know which way the electorate is leaning. Part of the reason why Democrats and Republicans are able to maintain a two party system is because they are so broad in their base. If they see some of their voters are straying from the party, they will adjust their rhetoric to get those voters back.
2. Federal Election Funds Are at Stake
Third parties don’t get federal election funds unless they meet certain criteria, one of which includes getting enough votes in the last election. If you want your third party to have a better chance next time, then voting for it and encouraging others to do so could result in federal campaign funding for the next election.
3. Better to Register a Protest Vote than Not Vote
If your choice is between voting and not voting, then voting is the best thing to do, even if your candidate probably won’t win. Registering your protest by voting sends a message that you don’t like the current choices. Failing to vote sends the message that you don’t care or you’ve given up and politicians can safely ignore you, since you don’t vote anyway.
4. The Republican Party Used to be a Third Party
Although it is rare, political parties can appear and disappear. It happened in 1856 when the Whig party was replaced by the Republican party. We are not forever shackled to a Democrat/Republican duopoly. But it would take people promoting other options.
5. Social Proof is Needed to Kick Start a Movement
People won’t jump on the bandwagon of a new political party unless they see others jumping on. If you want your political party to grow, you have to prime the pump by being one of the first voters for it. It’s how the Republican party came into existence. It started with a few people only and grew. And then it replaced the Whig Party, and instead of a Whig/Democratic duopoly, we have a Republican/Democratic duopoly.
So it isn’t a wasted vote, even if your candidate does not win.