the wiki says its a movement to establish a jew only land in current Palestine.

More or less, yes.

How come they have so much power over protestant countries?

Long story short, they proved themselves in the 1940s to be a powerful force in the region. The Middle East is known to be rich in resources such as petroleum oil, and it also has major trade routes like the Suez Canal (I'm sure you saw the impact of the Evergreen blockage) and land routes through Afghanistan, Iran, etc.. One can see how important the region is in China's Belt and Road Initiative. So, having a military outpost able to credibly threaten this region with overwhelming force is a very powerful tool for Western imperial powers like the US and (historical) NATO allies.

So, the Zionist Regime has influence over these countries because they want the Zionist Regime to help us keep power in the region.

CXORA mentioned the Evangelical Christianity aspect of it, which is real, but I consider that to be more the cultural propaganda reason than the underlying material reason.

A Jewish homeland being restored around Jerusalem is meant to be one of the signs of the apocalypse. Christians want nothing more than the world to end. Its a huge part of the religion.