Republicans directly oppose all of those things, because they are, at their core, bad people who are only interested in their personal wellbeing, not of what is best for this country.
I don't think you ever get a good answer to that because the answer is ambiguous. Asking why "Democrats" or "Republicans" do anything is asking about a straw man. Many individual voters will have a nuanced opinion about all of those questions. The way a lot of the questions are phrased presupposes Republicans don't care about those things, which I suspect is probably wrong for most.
I think many of those who identify as "Republican" or "Democrat" don't examine most of those points in any detail at all and just simply vote down the ticket. Their opinions are probably not going to reveal any useful information.
For the rest, my guess is its probably a fundamental disagreement about what government should be responsible for. Voting for the government to further some cause is inhertanly voting for parts of it's implementation. I think my libertarian bias is leaking through.