The question begs another question: what is "open-minded?"
Liberal versus conservative tags simply don't apply.
Social conservatives will look at issues such as gay marriage and say that marriage is an institution established hundreds or thousands of years ago, and should remain intact. Conservatives such as me, though, recognize the need for social contracts for those whose partners fall outside the realm of traditional marriage interpretations. Common-law marriages should recognize contracts such as Social Security, inheritance, life insurance policies, etc.
Fiscal conservatives aren't alone in their desire to protect their assets. Many outspoken Hollywood liberals hire attorneys to do their very best to keep their clients' taxes low. Progressive liberals talk about "fair" taxes. I would prefer to talk about minimal taxes for everyone.
The fringe of the Liberal Left supports the idea of free shopping carts and credit-card machines for the homeless in San Francisco. The fringe of the far right opposes any support for anyone who doesn't hold a job. Then there's those of us who think there should be a safety net for those whose lives have hit bottom. Not a handout for goldbricks, but a way to prevent peope from starving to death showing up on the streets. If nothing else, it's a bitch to have to step over them.
Both sides want to lay claim to the original intent of the Constitution and the Founding Fathers. The problem with those disparate views is that the language of both the Constitution and the writings of Jefferson, Madison, Hamilton and others don't leave much wiggle room. Parse the comma's all you want, but there is simply no doubt that the Framers meant for the American People to have the right to bear arms--all arms that the military possesses.
In that context, Liberals are more "open-minded," because they're open to ideas that run contrary to the foundations on which our country was built, and are more open to a "living, breathing" Constitution. Meaning that, at any given time, the Constitution means what they say it means.
Back in the 1950's and 1960's, conservatism was defined by the likes of William F. Buckley and Barry Goldwater. At that time, conservatism as we know it now didn't exist except for very few public figures. In fact, neither Buckley nor Goldwater or others even gave lip service to what the conservative movement is now: an almagum of religious conservatives, "gun nuts," border preservationists, and other groups.
On the opposing side, liberalism in its classic form embraced religious freedom (JFK's Catholicism was a huge issue in Kennedy versus Nixon, 1960), acknowledged the Second Amendment (and the other nine), and--in the North--embraced racial equality.
Interesting that the conservatives have been tagged as the racists in recent years, when it was the Democrats who largely opposed the Civil Rights Act of 1964.
What has happened since the late 1960's is that various groups with very specific intentions--and that includes us "gun nuts," as well as pro-abortion advocates, pro-life advocates, gay rights advocates, opponents of gay rights, fundamentalist Christians, fundamentalist atheists, and other groups--have had to go wandering in the Desert to find a home.
Once said home is found, a compact is formed with either the Dem or Repub party, and the volunteers and contributions start flowing in, it's impossible to stop.
Try running a real pro-life candidate in a Democrat primary, or a staunch atheist in a Republican primary. It ain't going to happen.
In other words, if you believe that it is your God-given right to own an M60 without any government intrusion, and that it's the right of you and your spouse to decide whether or not to abort a child, you're pretty much screwed by either party. Pick your #1 priority.
That's just one example, and a flip-side example would prove to be just as true.
We'd all love to see third or even fourth-party candidates get real votes, but without the money it's not going to happen. The two parties control the cash.
Back to the original question, though: my liberal friends are more open-minded, because they'll change their views frequently; I'm more close-minded, because I've tried to base my views on logic, history, and what I was taught was right.