Speaking only of the United States, I do not think that Christian churches are disproportionately right-wing. Some are, while other are demonstrably left-wing. I defer to those who actually are Christians to speculate about what political party Jesus would join.
During the American-Vietnamese War, cold war protests against American nuclear-weapon possession, testing, and deployment, and civil rights demonstrations, Christian churches were among the most prominent protestors, energetically advocating left wing-positions on those issues.
Pendulums swing, and now people more readily come up with examples of right-wing political activity.
So far as I can tell, the left-wing churches who were so prominent 40 years ago haven't gone anywhere, nor were the right-wing churches born only in the last 20 years or so. What seems to have changed is who gets more publicity, and maybe whose activities most sorely tick off those who disagree with them.
The Vietnamese war was a hot issue in its time. Abortion and stem cell is hot today. The left-wing view was the status-quo shaker in those days, while the right-wing view is the one that sparks more anger today.
Chrisitianity seems always to have been about ticking people off

. Right-wing, left-wing, whatever it takes.