You don't agree with equal rights and equal pay? You don't agree with a women's right to choose? You don't agree with universal health care? You don't agree with social safety nets?
These are not binary, yes/no issues. You can agree with these ideas, and still disagree about the best way to accomplish them. The Republicans support a social safety net too, but their idea of what it should look like (very small and largely privatized) is very different from the New Deal style liberal idea, which in turn is very different from the broader, more inclusive leftist perspective.
Trying to reduce these issues to "if you oppose the Democrats, you oppose (broad, generic good thing)" is not any better than when conservatives say "if you oppose our version of national security, you hate America." Political issues are almost always more complex than that, and it serves the debate poorly to pretend otherwise.
The most important one to me is healthcare. The Democrats' idea of "universal healthcare" is that everyone should be able to afford to buy private insurance. I think that's idiotic, and only fully support a single-payer system. That's not going to happen though. So, as a leftist, I have to decide if I can hold my nose, vote Democrat, and be okay with it. If so, great, if not, that's fine too. The lesser of two evils is still, by definition, evil, and there comes to be a point at which even the lesser evil is intolerable.
The only thing we're arguing about here is if we are already to that point with the Democratic Party.