Even if you disagree with the system, vote for whoever is most aligned with your values. Someone will want your vote and your decision may impact future campaigns.
The Tea Party isn't an actual party that fields candidates, its a right-wing grassroots (or astroturf, depending on who you listen to) organization that mostly backs Republican candidates, and mostly serves to push the Republicans on certain issues. If you vote for a Tea Party-backed candidates, a Republican has won your vote, not lost it.
I don't know that I agree. In practice, it's hardly happening (look at the Republicans and Democrats; at Trump and Clinton), and I don't see why it would happen.
Ideally candidates want to avoid alienating their base, but they also can't pick up more voters by pandering to them. So, everyone tries to appeal to independents and not energize their opponents base. The other strategy to to fight dirty which tends to suppress voter turnout, but that can easily backfire in a presidential election.
This also often results in coded language. Which lets you target messages to people that care about an issue without generally annoying other people.
Most recently is probably Libertarian > Tea Party. Not that they really had much impact, but people paid lip-service to the ideas.