Because anti-Zionist and anti-Semitic rhetoric is identical, both are damaging for the Jewish community.
Anti-Zionists often fall into the trap of perpetuating anti-Semitic stereotypes or tropes in their criticism of Israel and Zionism.
Two cases best illustrate this. The President of the National Union of Students in the UK, Malia Bouatta wrote a blog criticising the prevalence of Zionist thought in UK universities and the national media. In the blog, she referred to "Zionist-led media outlets". While her criticism of Zionism as a concept may be valid, expressing it in this language is damaging. It perpetuates the harmful myth that a Jewish conspiracy controls the international media. Ilhan Omar, the US Congresswoman, has also used damaging language in her criticisms of Isreal. She first accused American politicians overt support of Israel as being "all about the Benjamins", then in a panel discussion she accused Jewish lawmakers of having an allegiance to "another country".   This language is damaging because it echoes some of the accusations made against Jews by the Nazis and other anti-Semitic groups. Support for Israel is complex and reducing it to money, or going further and accusing Jewish lawmakers of having "dual loyalty", falls into the trap of using well-established anti-Semitic tropes to criticise Israel.
There is nothing anti-Semitic about the comments mentioned. Asking questions of the influence Israeli money has over US politics is a valuable exercise. Levying charges of anti-Semitism against anyone that raises the issue is little more than a tool to stifle debate over Israeli policy. David Steiner, the former president of the American Israel Public Affairs Committee (AIPAC), was caught on tape bragging about his role in influencing George H.W. Bush to increase aid to Israel in 1992. He also bragged about securing key jobs for pro-Israel politicians in the Clinton cabinet.  In another incident, in 1984, Senator Charles Perry refused to sign onto an AIPAC-sponsored letter and called Yasser Arafat, the leader of the Palestinian Liberation Organisation, a "moderate". AIPAC subsequently raised more than a million dollars and gave it to his opponent in the next election in an attempt to get him out of office. Questioning the influence of Zionist money in politics and the allegiance of politicians is not simply regurgitating anti-Semitic tropes, it is a necessary exercise given the evidence.
[P1] Anti-Zionists often use anti-Semitic language and tropes. [P2] Therefore, both pose a threat to the Jewish community.
[Rejection P1] They are not alluding to tropes. They are raising issues based on actual evidence.