This sounds like one of those classic stories where there is more out there. If you look at the complaint, they want 501(c)(3) status. That’s for public charities, not political groups. There are fairly strict rules about how much time and dollars can be spent on political issues. I suspect that has more to do with the IRS questions than the group’s Zionism.
Any issue that a lot of people feel strongly about ends up being a political issue.
There is nothing wrong with a public charity made up of zionists. However, if the organization actively engages politicians or directs it's members to do so, then it isn't a charity.
If you read the Complaint carefully, you’ll see that Z STREET is not a political group at all - it does no lobbying, it doesn’t support any candidates, and its purposes cannot be accomplished through legislation. A public charity is a whole separate issue, This group is an educational organization (a public charity is yet a different category. IRS regulations are strict, but they are not allowed to consider and make distinctions based on viewpoints, which the IRS agent said was what was holding up the application. And the First Amendment sure as hell doesn’t allow that!
They are not a political organization. JStreet, the pro-Obama (pro-Hamas, self-hating Jewish) group got fast 501(c)(3) approval. This is yet more Nuremberg Special Laws for Jews who don't obey The One.