For the reference, I'm a right-wing liberal / classic liberal / free market fanatic (lower right quadrant of the political compass). I shifted to the right after I started my studies in economics.
Which is the main reason why I disfavour the radical left progressives. While their intentions are just in many senses, their policies could seriously hinder or even push back the economy. Social justice is one thing, but giving up too much from progress in order to fuel equality will mean no progress and stagnation for all. And what feeds the campaign towards equality right now is progress.
I agree with rights of freedom. In some sense I'm over-the-border with the freedom of speech, meaning that I support the 'freedom of being a prick'. I think there should be no legal consequence for a weird opinion, only the condemnation of the peers. As soon as you silence an extremist opinion, you silence /an/ opinion and you destroy free speech.
However this also means the freedom of entrepreneurship, which in a capitalist world (and we live in one right now) is essential. The freedom of finding funding for your concept and fulfilling your dreams, be they creating a new social media site or a gardening store on the corner. And this is heavily hampered by regulations that would be imposed by the left wing, be it the wealth-redistribution or combating 'large firms' for whatever reason.
Civil rights, I agree on some and I disagree with others. Gay marriage? Not marriage, scrap the legal side of marriage and allow any partnership / household to have the same benefits, while retaining marriage ceremonies for the churches.
Wealth redistribution? I find that quite immoral and economically unstable and ineffective. Social mobility is far more important than wealth redistribution. Reward ambition, not stagnation.
Other issues ... can't really think of any. Feel free to comment some modern-day issues and I'll tell you my own views and my opinions on those who take it too far.
So, all in all summarised, there will always be radicals ruining the picture. But that's the same with Republicans or centrists. Yes, I believe in the existence of radical centrism.