That's just not so. The media has always been liberal, always biased and always against conservatives, at least since the LBJ Great Society days. There were left-wing movies made in the 60's and 70's too, more in fact. Vietnam anti-war, green propaganda, Soviet apologism and more.
The one thing that is constant and predictable in American politics is the liberalism of the media. It's simply a given.
Yes, there has always been a leftist slant in the media. My argument is that today, that slant is more pronounced and that media saturation is so complete, it could be described as ubiquitous.
In 1980, Ronald Reagan had the opportunity during the debates to really change the prevailing public opinion about him that he was a war monger and an idiot. He was able to change that opinion because before the advent of cable news, people only really had very limited exposure to the candidates themselves. So, while they had an opinion, it wasn't as resolute as the opinions that are held today.
This is why we did see wild swings in the electorate - huge landslide victories in 1964, 1968, 1972, 1980 and 1984. Then, almost perfectly synchronized with the emergence of CNN, the country started to become more polarized and fixed. It's also, IMHO, why we have only seen a Republican win the popular vote in a national election just once since 1988. The media is much more capable today, than they were in before the 1980s.
And, I would point you back to that list of Oscar movies. Look at the difference in the types of movies produced in the 1960s compared to the movies produced today. The politically-themed movies have increased exponentially.
With respect to television, All in the Family and MASH were unique in their era precisely because they were so political in nature. They were ground-breaking for just that reason. Today, as I said earlier, it's difficult to watch any show on any network that doesn't have some either overtly political message, or subtle political message.