Its hard to define.
I think most rational and logical people who aren't caught up in the whole "I'm a liberal" "I'm a conservative" game, have a mixture of beliefs of both.
My father-in-law for example, is an evangelical Christian - that should place him in the no-brainer category of conservatism, but wait, he's also a life long member of the UMWA (coal mining union) and a retired coal mining electrician, so that should put him squarely in the 'liberal' box because unions will always support liberal Democrats at the ballot box. He has very conservative beliefs at his core, but he will always vote Democrat because he was raised that way and it was ingrained into him over 40 years of working in a union.
My parents have conservative beliefs, my stepmom is an active practicing Catholic. The Catholic Church has a strong anti-abortion stance, but she always votes Democrat, and has been very active in the local Democrat party at times serving in different position. There's a conflict there because Democrats support a woman's right to choose. My parent's also believe in gun rights and a smaller limited government.
There's a disconnect that's hard to explain but I think it comes down to whichever belief you feel the strongest about and then go with whichever political party trumpets that belief the loudest.
This is only my opinion but today's conservative/liberal split is because the extremists of both sides are speaking the loudest and drowning out all voices of moderation and bi-partisanship from people in the middle.
Some time in the late 90's-early 2000s, Conservatives took over talk radio, and liberals took over the internet. The extreme partisans from both sides like to whip up people into a frenzy and try to divide and polarize as many people as possible. This brings them ratings, website hits, and ultimately lots of money. They have enormous power over their listeners, viewers, and readers, and they're always putting out a call-to-arms for their people to draw their pitchforks, take up sides, and go to battle against the other side.
I was born 3 months before Richard Nixon resigned, Jimmy Carter is really the first President that I remember. This period of American history, from around the year 2000 until now, is the most polarizing that I've ever seen this country. The country has always had partisans who shout from the rooftops and rally the troops, but with today's technology they can reach more people and mobilize faster. I also believe that the polarization really ramped up after the 2000 election when George W. Bush became president. Many democrats, still to this day, believe that he stole the election thanks to his brother who was governor of Florida, and caused all kinds of shenanigans to make sure that state went to his brother. They also feel he was ultimately handed the Presidency by the Supreme Court who had a conservative majority. That is when shit really started to get nasty in this country. At that point, I started seeing a lot of people who no longer had respect for the office of the presidency. I was raised in an era where no matter whether you voted for that particular person or not, to always have respect for the presidential office, but that is no longer the case, and this just sends the partisan hacks on both sides into bigger rage fits when they see their guy getting disrespected.