It has no power.
Corporations and wealthy donors have the power in both major parties. And corporations, whether they support Republicans or Democrats, almost unanimously take liberal stances on social issues. That's why social conservatives haven't been very successful.
Please reference the original post of this very thread.
Your argument about corporate donor power is reductionist and fails to take into consideration the nuances of American politics. Target allowing gender-identifying based access to it's restrooms is not a setback for the Dominionist movement, if anything it actually is good for them.
If you honestly think the Dominionist movement isn't a big deal in GOP politics, you just don't know what you're talking about. Or perhaps are being willfully ignorant.