From BBCs Editorial Policy, 4.4.5
"We must apply due impartiality to all our subject matter. However, there are particular requirements for 'controversial subjects', whenever they occur in any output, including drama, entertainment and sport.
A 'controversial subject' may be a matter of public policy or political or industrial controversy. It may also be a controversy within religion, science, finance, culture, ethics and other matters entirely."
So yeah, this guy did not 'toe the company line' as you put it, and broke conditions of his enjoyment. If I was the BBC I would be embarrassed. Embarrassed to have employed such a dullard whose opinions are clearly rooted in the Stone Age. And that's me being very unfair on Neanderthal man as I'm sure most won't have batted an eyelid at any child bearing woman breastfeeding.
The mans a twat, regardless of his right to free speech.