I know that in the era from 1950s-1980s, shows on TV were a whole lot cleaner, though. But do you think there was allowed more freedom on TV networks to "slip up" once in a while? Not to mention there are still some things in classic TV and movies from that era, that are considered taboo today. So, would you say modern TV is censored more or less than it was during the past?

Depends on the content. Sex was obviously more censored back then, but racial or religious language is probably more censored now than in our parents' generation.

The short answer is of course, more.
What is considered to be offensive changes with the times.
Im not aware of any religious censorship... there are hundreds of religious programs on tv.

I think he is referring to religious references on what we would consider "mainstream" TV and film.

My other point is that while things that were once considered offensive have changed, the government has always played an increasing role in deciding what is considered "offensive". That wasn't as true in the first decades of TV.

Things have gotten a lot looser with language and sex. What is new is the whole PC thing, but that is more media shaming and not the government disallowing it.
Also, Cable, Satellite and the Internet has completely changed the game.

It depends. On the first season of Saturday Night Live the censors allowed a sketch between Richard Pryor and Chevy Chase to use escalating racist words right up until the dreaded N word.

Archie Bunker, on "All in the Family" was frequently using derogatory terms for Hispanics, gays, Italians, Jews, and Chinese. You can't get away with that on TV these days, I don't think.

A whole episode of "The New Dick Van Dyke Show" was not allowed to be shown, however, when it dealt with Van Dyke's daughter walked in on him and his wife having sex.

Also, Richard Pryor was not allowed to appear in a body suit that suggested he was emasculated on his TV show.

Modern TV is virtually uncensored especially compared to the time frame to which you refer.