Blaming the evangelicals, regardless of whether there's an element of truth in it, is a diversion or a distraction IMO. The real reason for our policies toward Israel doesn't have much to do with religion or altruism. IMO, it has much more to do with money.
I think you vastly underestimate, probably naively, the role of Christian Zionism in the creation and the security of Israel. While Europe was in the process of disengaging from its historic colonial holdings, Western countries doubled down on their backing of a Jewish state in the middle east.
Benjamin Netanyahu knows:
"I don't believe that the Jewish state and modern Zionism would have been possible without Christian Zionism," Netanyahu said at the dedication ceremony. "I think that the many Christian supporters of the rebirth of the Jewish state and the ingathering of the Jewish people in the 19th century made possible the rise of Jewish Zionism."
I think it would also be naive to think that the evangelical belief in Zionism doesn't pay a pivotal role in our foreign policy towards Israel. It is a huge political pressure that nicely dovetails off the philosophies that helped create the Israeli state in the first place.
I would say is is the single most important component in our support of Israel and without it, our policies would be vastly different.