No, I do not believe that Republicans are conservative and all Democrats are liberal, because there is a wide range of what people are. Some Republicans are fiscally conservative, but are still against the death penalty. Some Democrats want a free economy but also want abortion. It all just depends. It's hard to classify.
Just as everything isn't black and white, everything isn't red and blue. I have a gay liberal friend who is a staunch pro-life advocate. Then there a Republicans who may be conservative when it comes to fiscal matters more so than social matter, such as gay marriage and abortion. It just makes the media job easier to paint us with broad political strokes.
I do not believe the political arena in America is black and white. Not all Republicans are conservative on all matters and not all Democrats are liberal in all areas. I personally identify as a Democrat. In my beliefs I am generally socially liberal and like a lot of socialist policies, but at the same time I am quite conservative when it comes to financial matters.
People can often confuse what liberal and conservative means, when it comes to politics. The media adds to the confusion when it constantly refers to democrats as liberals, and republicans as the conservative party. To be conservative, or on the right, means you want to keep things like have been or were in the past. To be liberal, or on the left, means you seek change. All though it can be rare, there are liberal republicans and conservative democrats.
Many people are registered into one political party or the other at a fairly young age, and political beliefs are rarely stagnant. Accordingly it's entirely possible for someone to take on a different political belief without changing their political party affiliation. Further different issues might make a person seek a party - a Republican might be economically conservative, but socially liberal - and accordingly the labels are less helpful than one might think.