The statement that I made about minimum wage has the effect that I describe because it is a major liberal-conservative argument. As soon as someone states a position on raising the minimum wage, everyone else around will tend to assume that they know their political position. I could have produced other examples ranging from approving oil pipelines to the wisdom of tax cuts to cost effective ways to produce health care.
Now you may be atypical. But most liberals/conservatives respond with the same pattern. They figure out whether you're with/against, and then respond emotionally. And the issues do not neatly divide on "intolerance".
More interesting, the dividing issues change over time. Today woman's rights is obviously a liberal issue. If you go back 100 years, allowing women the right to vote was just as obviously a conservative one, because women were a reliable vote for Prohibition, which was a thinly veiled tool to attack blacks, Jews, Irish, and other "undesirables". You can thank the KKK for helping women get the vote in this country.
The dividing line really isn't as simple as it seems at the moment. But it is sometimes easier to see this with the perspective of history.
You probably don't really think about the times a liberal person is reasonable and logical. You certainly will remember the ridiculous liberal who says illogical things.
Might that be skewing your impression of what 'most' liberals believe?