it's interesting that I make a post about certain parties being crazier than others, and everyone concludes that I mean the republican party. Doesn't that strongly imply that everyone on Less Wrong thinks on some level that Republicans are crazy?

That is a possible explanation, indeed.

Another possible explanation could be that everyone on LessWrong thinks that saying "my enemies are crazy" without providing specific arguments why is how Democrats typically speak. (Or perhaps that a Republican would likely use some other word, such as "godless" or "commie".) In which case, it's a simple logical deduction that if author speaks like a Democrat, his supposedly crazy enemies are most likely Republicans.

Yet another possible explanation could be that majority of American LW readers are pro-Democrats, therefore "crazy enemies" of a random person (in context of speaking of USA's two major political parties, which excludes Libertarians etc.) are most likely Republicans.

I'm not endorsing any of these views here; just saying that all of these are plausible explanations why someone might guess you meant Republicans, and the other explanations are not evidence for Republicans being crazy.

A different example: If you meet a guy on the street and he starts talking to you about "inferior races", are you able to guess whom he meant? Does your ability to guess correctly imply that you agree with him?