Republicans are a diverse bunch.  According to the Pew Research Center, Republicans and Republican-leaners can be divided into four main groups:  Core Conservatives, Country First Conservatives, Market Skeptic Republicans, and New Era Enterprisers.  Briefly:

Core Conservatives overwhelmingly support smaller government, lower corporate tax rates and believe in the fairness of the nation’s economic system.

Country First Conservatives are unhappy with the nation’s course, highly critical of immigrants and deeply wary of U.S. global involvement.

Market Skeptic Republicans sharply diverge from the GOP’s traditional support for business and lower taxes. An overwhelming majority say the economic system unfairly favors powerful interests. Most support raising tax rates on corporations and large businesses.

New Era Enterprisers are fundamentally optimistic about the state of the nation and its future. They are strongly pro-business and generally think that immigrants strengthen, rather than burden, the country.

Averaged across the above groups, 24% of Republicans surveyed by Pew considered economic inequality to be a "very big" problem, compared to 62% of the Democrats surveyed. 

One thing I gained from reading the Pew report is some insight into why Republicans and Democrats think so differently about inequality. It's not just a matter of different "values" - a lame explanation at best. Republicans and Democrats are both soft-hearted about some things and hard-hearted about others. What is it about inequality that triggers a soft-hearted response from a lot of Democrats and a less soft-hearted response from a lot of Republicans? Saying that one group is simply more compassionate than the other won't cut it.

The following chart provides a clue as to why the issue of inequality is not such a big deal to many Republicans:

Republican Groups 2017.png

What stands out for me is that, overall, Republican households are doing better financially than their education levels suggest. Many have done well despite not having a college education. These individuals weren't handed the good life on a platter - they had to work hard for it, against the odds. It's enough to harden the heart a bit against those who claim they've been kept down by an unfair system.

Not a complete explanation but points us in the right direction.

Reference:

Pew Research Center, “Political Typology Reveals Deep Fissures on the Right and Left” October 2017