The Unruh effect is theoretical, and no evidence at all has ever been found that it's real. It literally exists as nothing more than a hypothetical mathematical model, that also happens to be debated by others who know enough to effectively debate it, and disagree.

Why ice?

It's one of those cases where you have very small numbers multiplied by very large ones. The actual risk is hard to intuit because there are so many orders of magnitude involved in both directions.

In any case it's probably a moot concern as long as we are living under the twin tyrannies of Newtons Third Law and the Rocket Equation. Building a rocket that can accelerate constantly and noticeably for weeks, months, or even years on end in order to accelerate up to a velocity where Relativity starts to matter requires an absurdly large rocket. Like converting the mass of Jupiter into rocket fuel to make it to the next habitable solar system in a couple of centuries level of craziness.

But it's also very big, and GP doesn't even specify how far of a trip they're asking about nor how small a meteorite.

"Extremely" and "very" don't cut it here. This is beyond the human ability to guess. You'd actually do at least some back-of-the-napkin math to give a real answer, and with a far enough trip, the answer may well become "Almost 100%".

Micrometer-scale dust particles would in fact hit you all the time. And they’d absolutely mess up your ship over time without a lot of shielding.