I think it's wrong to suggest that opposition to Obama's agenda is "race-based," because that suggests conservatives would feel differently if Obama weren't president. I think the GOP's general positions on the issues would be the same if Hillary Clinton were president.
What's clear, though, is that conservatives deploy racially tinged rhetoric against liberal policy priorities and Democratic politicians, and that Obama being president has a lot to do with these arguments being used. Rush Limbaugh wouldn't be comparing him to gang members if he weren't black. With Clinton, Limbaugh's sexism, rather than his racism, would be amplified. So while it might be unfair to suggest people are conservatives because they're racists, it's entirely fair to ask why conservatives are comfortable with their most prominent ideological figure's casual use of racism as a political bludgeon.
A secondary question is whether the constant invocation of the president's race in the context of political criticism alters conservatives' perceptions of racial minorities in general. Limbaugh's racialized criticisms of the president lead the listener to some very ugly conclusions about black people as a whole.
