Earlier quoted context omitted.
While as argument, it may work, it does not seem to be conservatives that are afraid of AI ( at least in public fora ). But that is separate from your point on class type ( the rich ), which seems to be reason why it does not land well ( for me at least ).
The reason why this seems weird to you (and many other people for sure) is that current "conservative" politicians are actually more neoliberals than conservatives. So of course they will push cheap labour, offshoring, outsourcing and eventually AI. But it shouldn't be hard to understand actual conservative ideology here, since, like, it's already in the word.
You're wrong about the other side of the aisle, though. People who are otherwise pro immigration, pro social change, pro downwards wealth redistribution, etc. (in other words, not at all conservative), are typically against AI.