It's mostly just rhetoric...things they say at any given moment that they think their base wants to hear. So when liberals talk about feelings of say marginalized groups, conservatives will wave that away with things like you mention ("facts don't care about your feelings").
But when the facts aren't what conservatives want, you get the opposite, such as Newt Gingrich saying that he'll go with feelings over facts, Giuliani saying "truth isn't truth", and Kellyanne Conway saying (after being shown wrong) that she's presenting "alternative facts".
It's basically whatever suits their needs at that particular moment.