Of course they don't, the Nazi card is a far-right concept. The far-left analog is communist, and they did plenty of that during the "red scare." They still use "communist" or "socialist" terminology to write off opponents.

And no, the Republican party isn't actively courting neo-nazis, it's neo-nazis that are using Republican talking points to appeal to a broader audience. There's certainly a venn diagram overlap there, so Republicans can appear to be supporting neo-nazis, but that's really just neo-nazis trying to appeal to more of the mainstream.

Don't get caught up in the partisan name-calling, it sucks when Republican do it, and it sucks when Democrats do it, it's just a really stupid version of a strawman. Democrats don't want to seize the means of product but Republicans want you to think they do, and Repbulicans don't want to kill minorities but Democrats want you to think they do. Don't buy in to the divisiveness BS, look at the facts and make your own decisions from there.

I personally hate both parties since neither actually deliver on the parts I like from their platforms, and they tend to behave similarly on the issues I care about (e.g. both largely support Israel, both seem happy to continue undeclared wars, both seem happy to run up deficit spending with little to show for it, etc). Screw the two party system and "pundits" in general.