It's very difficult to characterize this as an isolated incident of anti-semitism by the BBC considering it's far from their first incident, and considering further that the BBC has spend 20 years and well over £300,000 keeping the 20,000 word Balen Report into their perceived anti-Israel bias buried.
How can we be expected to believe that there is no anti-semitism at play when the BBC claim that they refuse to call Hamas a terrorist organization because 'Terrorism is a loaded word, which people use about an outfit they disapprove of morally. It's simply not the BBC's job to tell people who to support and who to condemn [...] We don't take sides. We don't use loaded words like "evil" or "cowardly". We don't talk about "terrorists".' despite the fact they actually do that constantly, and have for decades?
Rajib Karim: The terrorist inside British Airways
Brussels: Epicentre of the terrorist threat in Europe?
Built at a time when IRA terrorist attacks were a constant threat, High Point was built to be bomb-proof
Securing and maintaining reliable funding is the key to moving from fringe radical group to recognised terrorist organisation
Eighteen years after the Brighton bombing, former IRA terrorist, Patrick Magee, has continued to defend his role in the blast
[Lisa] Smith was, however, found not guilty of financing terrorism by sending money to a man for the benefit the terrorist group.
Sudesh Amman: From troubled schoolboy to terrorist
Between 1969 and 2001 over 3,526 people were killed in terrorist violence in the UK. ↑ this one is from BBC Bitesize, educational material the BBC writes for children. I guess editorializing to children doesn't count as taking sides.
The BBC clearly has no problem naming and shaming terrorism when Jews aren't the target. This assertion of "Jewish wealth" isn't only an obvious Elders of Zion appeal, it's the latest in a long, long line of Isolated Incidents of the BBC suddenly altering its established reporting standards for only the situations where they address the one country in the world full of Jewish people.
Your second point is entirely correct; see also self-hating gays in the Log Cabin Republicans.
I think the shield for your first point is pretty narrow these days. About a decade ago that point held a lot more salience, but as my "new antisemitism" link discusses, the position has been adopted so vigorously by antisemites that I think it is indeed very close to antisemitic unless deployed extremely carefully.
Yes, criticism of Israel is not inherently antisemitic. But since this canard is so often invoked by idle and ignorant spectators, with no real understanding of Israeli or Palestinian politics, inserting themselves into a fraught and unhappy situation, usually specifically to criticize or delegitimize only Israel... it's tough to see how that isn't a special standard applied only to Israel. Or, worse, it's invoked by real antisemites hoping to get bystanders on-side with actual antisemitism by cloaking it as criticism of Israel.
As a concrete example of this new antisemitism -- in 2017, Hamas altered its charter, which was wildly and outright antisemitic, to specifically state that it doesn't actually want to kill all Jews as previously stated, but only the occupiers of Palestine. Given their actions, the huge amount of specifically anti-Jewish sentiment in Gaza, and even the incredibly virulent language in their old charter, do you think they actually changed their minds about Jews? Or are they simply cloaking their antisemitism in a package that more people might agree with these days? A new kind of antisemitism?