white supremacist subreddits like /r/europe are pro-Israel, probably only because it conveniently resonates with their anti-immigrant and anti-muslim messages.
The pro-Israeli stance of a Europe that is as antisemitic as it always has been is no new thing - even the Nazis considered forcing Europe's Jewish population to emigrate to Palestine as a potential "Final Solution" to their precious "Jewish Question" (it was dropped as a "solution" because Palestine was in British hands at the time). Christian Zionism predates Jewish Zionism - and it was always firmly based in European antisemitism... ie, the (very antisemitic) idea that Jewish people are "other" and cannot belong in "western" society. People are quick to forget - the post-WW2 era was the only time in "western" civilization's history that overt and brutal antisemitism wasn't the order of the day. From a historical perspective, it might even be considered an aberration for "western" society - and, considering the resurgence of of overt far-right ideology in the Global North, it may be an aberration that is coming to an end.
It’s like saying the people that support Palestine do so because they’re anti-Israel.
but the common people do it because of how close their values and culture are to their own.
What "values" and "culture" would that be? A belief in "western" superiority as catalyzed through genocidal settler-colonialism? White supremacism, perhaps?