Good principles Republicans have (interpreted to make them as good as possible):
1) American/Anglo/Western values are objectively good and it would benefit people in other cultures to learn them.
2) Morality is important.
3) Sometimes you have to stand up for good values, and even fight for them.
4) Good traditions should be respected. That means people who wish to change them should understand them and their value, and suggest only well-thought-out improvements which they can reasonably expect will do no harm.
5) It's good for people to be competent to take care of themselves, and to take responsibility for themselves, and to take pride in running their own life.
6) People should voluntarily be friendly and help each other out.
7) There is evil in the world and closing our eyes will not vanquish it.
Interesting. These seem to be weaker statements than the ones about Democrats. Morality being "important" says little about directionality; the notion that one has to stand up for "good" values merely begs the question of what those are. Ditto for "good" traditions (Social Security and progressive income tax rates are, by now, traditions; are they "good"? Because Republicans tend to oppose them when able).
These do seem to be good principles to me, but squishy ones with a lot of give that are hard to defend when the rubber meets the road, i.e. in some particular situation. So, maybe that's the root of the (R)s' problem.
Republicans do have an idea of what morality says, and what are good values (and their view is common knowledge). On a lot of points, democrats would agree. The larger difference, imo, is not in which values one holds, but what attitude one has towards values. Republicans consider values very important. Leftism seems to be wondering if morality exists at all, and, if it exists, whether it's objective or just cultural baggage.