Poppin, conservative neo-liberal can refer to one who holds conservative values as well as neo-liberal ones. Generally speaking neo-liberal refers to more economic principles such as free markets. For more info in a nutshell:
Neoliberalism - Wikipedia, the free encyclopedia
The point I was trying to make in my first post is that these things are not perfect binaries, not black and white. Not all traditional labels such as left, right, liberal, conservative, socialist, capitalist fit perfect molds. Far too often, discussions get bogged down and jammed up due to preconceived notions regarding these labels. We effectively handcuff ourselves intellectually and stagnate in thought.
For me, I believe in a capitalist economic system comprising of free markets and minimal government interference. The problem with the way the op is framed it is reduced to extreme poles without nuance or meaningful analysis. I do no believe in the extreme view of capitalism nor free markets. That is just unwise and impractical. Basically, I believe in a system of minimal rules and regulations that still allow free enterprise to flourish but not at the expense of humanity. I think that's a significant point. For example, I am against reckless drilling of oil and wanton establishment of factories and plants without regard to the environment. I also believe people should be paid a fair wage but the market should decide.
Some legislated social benefits I would be willing to support such as health care, basic education depend on administration. I think this is also a significant point. I simply do not think the government has been competent enough to carry out these benefits like the private sector can. Somewhere in the middle lies a great solution and compromise. This I believe.