The best way of handling mindkilling is to look at hard data.

To some extent you may have a valid point, but parties are extremely diverse entities. Even if one looked at small, fringe parties, there's heavy variation in the beliefs. So, you might have a more valid point if you said something like "Self-identified Republicans are on average more likely to believe crazy things than self-identified Democrats." Now, this will run into other issues because party identification if fluid, but it would be a start.

So, let's use some beliefs that are by a largescale consensus "crazy" that are stereotypically associated with specific ends of the political spectrum in the US. I suggest the following four: "Barack Obama is a Muslim" (associated with the right), "The government was involved in 9/11" (left). It would be interesting to look at others that are more straight scientific issues, such as homeopathy works (left), vaccination is bad/causes autism(left), evolution is wrong (right). Now, let's look at the data, but I don't have the time to do so. So let's focus on the two essentially conspiratorial claims.

The most recent poll I can find for Obama being a Muslim is here. Approximately 30% of Republicans think that Obama is a Muslim. Curiously, approximately 10% of Democrats think Obama is a Muslim (this is likely connected to the fact that 5-10% of any poll will be extremely confused or just give nonsensical answers).

Unfortunately, very few of the polls about beliefs about 9/11 ask for party identification, but there's a Rasmussen poll indicating that around 35% of Democrats answered yes to Bush knowing about 9/11. See here. They don't state the actual percentage of Republicans, and the actual poll seems to be behind a paywall. Moreover, other polls have gotten much smaller total percentages of belief, so actually getting data here may be tough. But at least from these two, it looks plausible that about an equal percentage of Republicans and Democrats are being crazy for their thing (although slightly higher numbers of Republicans may be saying yes to the Democratic brand of crazy, that's hard to really tease out from the data, given margins of error, differences in questions, timing, and other issues).

Now, you can argue that there's a difference in how seriously these beliefs are taken by the leadership in each party. So what's the highest ranking politicians who have said that Obama was a Muslim? Well, it is easy to find high-ranking Republicans who think that Obama is getting advice or orders from the Muslim Brotherhood. Louie Gohmert is one of the louder examples. But that's not the same as claiming that he's a Muslim. So let's now look at the reverse. The closest analog for the 9/11 issue then to Gohmert would be people wanting a new investigation. It turns out that's a pretty large set . See here. It ranges throughout the political spectrum, and it isn't easy to tell without much more work which of those want a new investigation because they think the 9/11 Commission didn't do a great job and how many want a new investigation because they think it was the Illuminati/Rosicrusians/Jews/Daleks etc. So, actually looking at this metric may be tough.

Note it occurred to me while doing this, that birtherism might have been a better analog than claiming that Obama is a Muslim, and one does in fact get high-ranking politiicans endorsing that. See e.g. here. My impression is that genuinely crazy ideas are much more likely to be taken seriously by leadership on the right than leadership on the left, but getting substantial evidence for that is likely to be tough..This data at least suggests that any different between the two among the party base is small. It would be interesting to look at a bunch of other issues in a systematic fashion. While that would be fun to look at it, it wouldn't by itself say much of anything about on any specific policy issue where Republicans or Democrats are correct.