How does the coriolis effect affect airline navigation?

I go out to dinner and everybody else hits this one out of the park. Yaay!

Simply stated, Coriolis acting directly on the airplane is utterly swamped by wind acting on the airplane over the same time interval. And yes, a lot of why the wind is blowing the particular way it is is itself a consequence of Coriolis.
The rotation of the earth does have a very real impact on inertial nav systems though. Once spun up the inertial nav “platform” is stable in 3-space. If you were sitting stationary on the ground on the equator and waited 6 hours, the platform that had been aligned to pointing straight up (=local vertical) would now be pointing horizontal to the ground. And 6 hours later would be upside down.

So this earth rotation needs to be compensated for even if the airplane isn’t moving. A similar issue arises in another direction if the airplane *is *moving. Here’s a bit about that: Schuler tuning - Wikipedia
Here’s another consequence of a rotating Earth:

During the start-up process for the INS platform, it needs to be told where on Earth it is. The alignment process typically takes about 10 minutes. During that time the mechanism compares the motion it’s “feeling” from the Earth’s rotation with the motion it expects to feel based on the latitude provided. If those two values are too different it assumes there’s a problem; either a malfunction or an invalid starting position was entered. And the system will not transition from “aligning” mode to “ready to navigate” mode until the disconnect is resolved. That’s also why the aircraft can’t be moved even a smidgen while the alignment is in progress. I’m not sure how the Navy solves this problem when aligning aircraft INSs on a moving ship.