No, you can't donate directly to the IDF, but turns out you can just make stuff up as long as it fits one's world views.

There's a lot of people making this stuff up on the internet then.

Yes you can donate (why did you add the word "directly"?). It just passes through intermediary organizations, such as the Friends of the IDF. There are even non profits that pay for "lone soldiers" -- international mercenaries -- to take part in the genocide in Gaza. Hundreds of thousands of "lone soldiers" took part, I believe something like 20,000 came from the US alone.