Firstly, they're typeically at the start and end, so the show runs continuously in the middle. The only exceptions I can think of are some of the comedies and variety shows. Listen to some of the Sherlock Holmes episodes. Dr. Watson converses with the Petri Wine spokesman at the beginning and end, and sometimes to move the plot along. But it never disrupts the drama with blatant advertising.
Secondly, since the actors in the shows were often quite talented, having them spend a thirty seconds about the sponsor is not annoying and sometimes genuinely entertaining. I'd much rather listen to Groucho Marx sing the Plymouth Desotto song than any of the modern radio or tv advertising.
Thirdly, the ads from then actually presented the product and its merits. Nothing was "extreme" or "edgy". They were simple, informative and to the point. It's far easier to digest an advertisement that's not annoying.