Has anyone seen an anti-vaxxer argument that isn't insane?

That's a bit of a no true Scotsman, I suspect. There are plenty of sane reasons to not get vaccinated, but you're gonna say "that's not antivaxx!"

A few of us decided early on to not get vaccinated quite yet because there was a loophole that allowed us to get our shots, which would have taken them away from people in far higher risk categories. A few months later, we all got our shots.

Some people really do have super adverse reactions, and live in low risk areas.

The immunocompromised.

Being opposed to vaccines that aren't necessary, like for rabies pre-exposure.

Being opposed to not yet approved vaccines, like kids under 12 or whatever.

Of course, all those are rational reasons, and therefore, not antivaxx. Antivaxx is basically defined as irrational opposition to vaccination.