Responding to Israeli author Amos Oz, Rabbi David Kaufman agrees that there is more than one way to be a good Zionist, but notes that this does not make it impossible to be a bad one. He references a page at his website articulating various ways that "pro-peace and pro-Israel advocates" sometimes act "harmfully".
The claim that one can purport to be pro-Israel, and yet act or advocate in ways that do it harm, is fair enough. But it has to be an even-handed principle, and there is little evidence that it is applied to right-wing Zionists, as opposed to only their left-wing peers. This is unjustifiable -- right-wing Zionists are guilty of many of the flaws Rabbi Kaufman identifies, and deserve the same level of chastisement for their breaches.
For example, while Rabbi Kaufman forbids "Criticizing Israel When Israel Acts to Ensure the Safety of Her Citizens", the prominent right-wing Zionist Organization of America has repeatedly done just that, attacking heightened security restrictions at the Temple Mount which place some level of burden upon observant Jews. This is hardly an isolated incident -- several years ago, ZOA demanded Israel apologize for its withdrawal from Gaza -- undercutting a prominent Israeli security determination that maintaining the occupation was damaging both to Israel's long-term security and democratic posture.
It is likewise notable that while the post singles out the BDS movement as inherently anti-Israel (perfectly fairly), it seems to give a free pass to one-stateism. The permanent transformation of Israel into "one state", from the river-to-the-sea, would quickly cause it to lose either its Jewish or democratic character, and thus bring about the end of Israel as we know it. For that reason, the mainstream Jewish position is that one-stateism is inherently anti-Israel (this is, for example, the position of the ADL and AJC), and groups that have hosted or tolerated one-stateism are generally considered to be intrinsically outside the boundaries of the pro-Israel camp. However, promoting a one-state solution is conspicuously absent from Rabbi Kaufman's post -- a silence that echoes throughout the Jewish community at large while one-stateism goes mainstream. One can't help but wonder if that's related to its growing traction amongst some right-wing elements in the "pro-Israel" camp. Mike Huckabee and Rick Santorum recently endorsed a one-state solution, and South Carolina, Florida, and the Republican National Committee recently passed a ZOA-sponsored resolution likewise promoting a "one state" outcome. In defending a position that most Israelis and American Jews think is intrinsically incompatible with the preservation of a Jewish democratic state, this would seem per se beyond the borders of acceptable conduct by pro-Israel actors -- and is generally recognized to be so when the call is made by leftist persons who desire a one-state solution.
There are other problems with Rabbi Kaufman's post: Many of the admonishments are either too vague to constitute workable standards or are expressed in absolutist terms that are unworkable. For example, is it "unilateral concession" for Israel to cease all settlement construction if one believes that the settlements are bad for Israel as well as Palestine? Why should we have to wait for Palestinian permission before advocating for policies we believe are in Israel's best interest? A right to self-defense is never "absolute" and nobody actually believes that it is (I can't nuke a city because of a single gunman), nor is taking such a philosophically absurd position necessary to recognize Israel having a vibrant and muscular authority to defend itself. In general, it is highly subjective when rhetoric becomes "demeaning" or "obscuring" or "careless" -- leaving a lot of room for biased application.
Even still, I don't disagree with the general sentiment. A bare assertion of good intentions is not sufficient to render a policy program "pro-Israel", and we need to have the space to call out people who stray from certain broad but recognizable boundary lines. But it has to be a two-way street. It can't be the case that right-wingers are free to be Zionist however they choose -- even when they criticize Israeli security determinations, even when they advocate a one-state solution -- while their leftist peers are constantly put under the microscope. There are borders on both sides, and we can't place one under stringent surveillance while leaving the other entirely unpoliced. One can claim to be a Zionist -- even a right-wing Zionist -- and still be a bad Zionist.