The role of evangelicals in the US Israel policy is highly exaggerated. Many jews who are worried about anti-Jewish sentiments like to emphase this connection to dilute the real actors in this front. People like the author of upcoming documentary(Jewish), publisher/chairman of your first link(Jewish), founder/editor of the second link(Jewish) really don't want American peasants to blame them for the US Israel policy and it's outcomes. It's much more convenient for them if white christians can be blamed somehow.

Strongly pro-Israel Jews are a large donor base for both of the parties. 25% of the billionaires in the US are Jewish, and an even greater percentage of the big donors to both political parties are Jews. Coming from just 2% of the US population, this is highly unrepresentative. Non-Jewish big donors like the Koch brothers are often unconcerned about Israel and can even have non-pro-Israel positions. Meanwhile having a pro-Israel policy is a central goal for many Jewish donors(Saban, Adelson).

Israel is not a big issue for most evangelicals and when polled, they don't mention it as an important concerns. They might have pro-Israel positions, but they don't vote on this issue. The more extreme evangelicals who do care about Israel have a miniscule amount of power.

I suspect Trump's pro-Israel jewish son-in-law and Sheldon Adelson(his biggest donor) play a much bigger role in his Israel policy than the 20% of Americans who are evangelicals.