My take on this question is a little different.
Discussions on the effectiveness of tax policy aside, the facts are:
In the US, Conservative legislators promote and enacts policies of lower taxation on the wealthy.
Conservative voters support these policies.
Conservatives have been shown to score high on Authoritarianism beliefs.
In my opinion, the observed support of lower income Conservatives for lower taxation of the wealthy is an expression of the Authoritarian mindset. The lower income Conservatives perceive the wealthy as “better” and “powerful” - as Authorities. And, to them, they deserve praise and more importantly, adoration - they are objects of affection. And much like the proverbial images of old, they feel good about paying tribute to these powerful figures (laying riches at the feet of the King). Maybe, because they feel that will keep them in their good graces? 'Dunno.
Consequently, any attempt to raise taxes on them are seen as attacks on their adored betters.
It’s not about logic, or “against their own best interests”, or economic / fiscal beliefs, it’s purely emotional reaction to how they perceive that the objects of their affection are being treated.