I used to think Jeremy Corbyn was an anti-semite. I also used to think Roald Dahl was an anti-semite.
But after researching what they actually said, it's clear that they were just smeared, because they weren't racist enough against Palestinians and (shockingly) thought Palestinians deserve human rights.
Honestly, I am now highly skeptical whenever someone calls another person an anti-semite.
I think the government or the Labour party updated their definition of what anti Semitic meant to include any criticism of the Israeli government a few years ago, which also says a lot.
I can't comment on either of them, but I agree with your last point and I will absolutely forever be suspicious of anyone labeling others as antisemitic.
It's like when white Americans brand a political movement or activist as racist. You know they're likely full of shit and you just need to do some very light reading before it all falls apart.