What are the principles of the Republican party that are correspondent to a 'good' latter day saint and what are the principles of the Democratic party that are not correspondent to a 'good' latter day saint.
It should be noted that the original question begged by the OP has not been answered which is: what is it about what John Birch (society) and the others stand for that are so bad?
As for the Republicans, it's simpler to say there is virtually nothing they stand for that is doctrinally opposed to the LDS Church. The same seems to apply to other conservative parties.
As for the Democrats, their core values and modus operandii are in opposition to the LDS Church. Socialism and the welfare state. Support for alternative lifestyles (such as homosexuality) and other immoral behaviors and beliefs (such as third wave feminism and above). Opposition to the death penalty is also contrary to LDS doctrine as well as support for abortion as a general method of birth control. Makes no difference whether or not the Church involves itself politically on these things. Comparison with doctrine is the order of the day.
Obviously not all Democrats support all these contrary things. But there is also the principle of Romans 1:32 by which I don't mean the death penalty for these sins (except murder), but rather the principle that those who vote, vote organizationally, or give money and public support for those supporting these behaviors and beliefs are just as guilty.
It is absolutely not possible for a good Mormon to be a Democrat, good or Dino.
I'll reiterate, I'm not discussing parties, but principles, values, and core philosophical positions. It's late, but I'll deal with this perhaps in another thread, where the discussion can look at your question on a point for point basis.
"Democrat" is a useful and precisely accurate catchall term. Much easier to type than the whole list.