I've always considered myself blessed to be able to place myself in the mindset of an era before watching a piece of older media. Whether it's a silent movie, a piece of 1960s TV or even newsreels, I find it very easier to put aside the differences in culture and age and watch them with a free mind.
I do understand why there is this kind of "barrier" there for some younger viewers though. Not everybody can make that "leap of faith", and look at things in the context of their era, even when they are activiely *trying* to do so. This is getting especially harder with how far drama has moved in the last ten years alone. The dissonance is getting larger all the time.
I think ultimately it's a personal taste thing. Some people just can't get their head around old stuff, while others find modern drama baffling, and a third group can watch both. No shame in any of it.