I'm confused too, and I often self-identify as conservative.

Part of the problem is you think there is unity in any large movement. There is not, only tiny movements with no political power have unity. There are multiple factions is always the right answer and you have to understand each. As a short cut, many (often the majority) are willing to live with those in their midst but don't actually care.

Fossil fuel companies have long supported conservative positions. This is their payback, they get support back.

Many do see renewables as the "left", and so they don't care to think, they just oppose anything the left does. (you often see the reverse)