By contrast democratic ideology is becoming increasingly authoritarian in that there's extremely little tolerance for views outside the party line. You'll generally find something like 85%+ support for the party line on most any 'hot' issue. By contrast, you'll find much more diversity in 'republican' views. For instance 'gun control' is supposed to be a black and white division, yet you find 31% [2] of republicans support stronger gun laws and only 13% would support less strict. By contrast, and as usual, you find a whopping 87% of democrats supporting stricter gun control and what measures as less than statistical noise (3%) in support of less strict gun control.
So there isn't really any such thing as a 'republican.' I think 'conservative' also does not necessarily apply ubiquitously, but it's somewhat reasonable. By contrast there is very much a thing as a 'democrat' and the vast majority of people that vote for that party are indeed 'democrats'.
[1] - https://thinkprogress.org/pro-choice-america-majority-d89630...
[2] - https://news.gallup.com/poll/243797/six-americans-support-st...