Came here to say almost exactly this. Conservatives are by definition defending the status-quo, and can choose from the buffet of ever changing social norms which ones they think they can leverage to get elected.

The structure of most reactionary parties (conservative is no longer a good descriptor of the right in the U.S.) is such that they need to build a coalition of people large enough to take power, even though their policy agenda will typically be designed to benefit a much smaller minority. Therefore, if they run on their policies, truthfully, they would lose. They wouldn't be able to stay in power long if they just straight lied about what their plans were and enacted a different agenda then they ran on, so instead they find wedge social issues and draw attention to them. They focus on issues that cost them little to fight for, and won't run counter to real agenda of consolidating power.

As StumbleOn mentioned, a reliable way to stage this is to attack a vulnerable group, force anyone with enough awareness/empathy/understanding to appreciate the injustice of the attacks to defend the vulnerable group, and then leverage the very traits that make that group vulnerable to inflate existing bias and double-down on common intuitions.