Is it permissible to continue a marriage that was contracted with a "partisan" woman who refuses to leave her religious political party and demands that her husband compromise on some of his beliefs, knowing that the husband follows the Salafi methodology and had agreed with her to prioritize the authentic text and evidence?

We advise delaying consummation with the wife because methodological differences could lead to separation later. Separation before consummation is better if the wife does not wish to follow the husband's methodology. The period before consummation is for testing her willingness. If she insists on her methodology, then she is not suitable as a wife, because the fundamental principle is for the woman to follow her husband. If she desires to follow the methodology of Ahl al-Sunnah (definition), then be patient with her and guide her path. But if you are not attached to her and you see her insistence on her opinion, then separate from her now, because such relationships inevitably lead to separation, and separation at the beginning of the path is easier.