I question your objectivity judging what the left and right do or don't do. Both sides have their bad moments when it comes to the "big tent" approach, but there are plenty of examples of lefties and righties embracing different viewpoints. The attraction of claiming "tolerance" for your personal ideology is appealing, but probably leads to inaccurate assessment of how tolerant people on your "side" really are. Particularly when your survey technique is to exclusively search for stories of the other side being intolerant
If you want a good example of where both sides need massive improvement, all you have to do is look at the hot button issues of the day. A politician taking the "wrong" side on an issue like that will result in them being absolutely destroyed by their party in most cases. Being a pro-gay marriage or anti-gun Republican or an anti-abortion or pro-torture Democrat will make things very hard for you.