You still vote for the lesser evil? Sitting out only benefits the greater evil, not you. I don't know how to make this any clearer.
What you’re arguing for is only single-round optimal, but multi-round suboptimal — much like defection in the Prisoners Dilemma is defeated by trust strategies the Iterated Prisoners Dilemma.
Until you show how it’s multi-round optimal, you haven’t addressed their critique.
Right now it looks like you drained the baby with the bathwater.
My bigger question: Why would you make the foreign issues dominate your national issues?
But to answer the first, I’ve heard directly from party strategists that they look for people who vote, but not in a particular race. They can’t identify them directly, but a higher ballot submitted count than (eg) presidential vote count is a signal that they can gain voters in that area — which they follow up by surveying independents, etc to see what policy issues they’re concerned with.
The argument is that by not voting some rounds, you influence their platform in subsequent rounds. If you vote for them regardless, there’s no incentive to optimize their platform to address your concerns.
What you're advocating benefits the greater evil ten times as much over a 20-year timespan. They're absolutely loving you. The more Bidens, the more Harrises, the more Clintons, the better for them.
You know why China is doing so well? Because they still remember how to think in the long term.