There are two types of Christians in this regard, Christians that get a government check, and Christians that do not rely on a government check.
Government is a convenient way to justify dancing around Biblical Commandments like “stealing” as we are surely doing from hard-working people and future generations.
So in my opinion, you won’t get much traction.
Same goes for “Conservatives” - there are those who get a check from Uncle Sugar in some form, and there are others who do not.
Government today perverts both Conservatism and Christianity, which is by design, I suspect.
So I think You’re asking the wrong question.
You are absolutely right about how one’s opinions regarding the proper role of government is highly correlated with the direction of cash flows. I’ve noticed marked changes in the opinions of people I know as they transition from taxpayers in their late fifties to tax recipients in their mid-sixties.
WRT “Government is a convenient way to justify dancing around Biblical Commandments like “stealing””: I’d argue that government is even worse in that it also actively encourages and even celebrates the envy forbidden by the 10th Commandment.