The right wing of america and the various christian cultural movements/monoliths have been allies since roughly the reagan campaign. The power of that alliance is a large part of the republican’s base/power. The politicians on the right have a great deal of push on them to parrot christian talking points, like the satanic panic of various flavors that was pushed about music and activities like D&D.

So while the d&d being evil may not have started as right wing propaganda, it quickly became so due to the way the cultural onus of christianity pushed politicians into acting. You can see the same thing with ‘christian’ values around political fighting with abortion, teenage pregnancy / sex education, israel (though that one is obviously much more complicated than just ‘church leaders fetishes -> politicians’ stances), ‘morality’ based laws around prostitution and gambling, etc.