The news has to be reported as is and without bias. If some find that offense, that is their problem and not the news network. Don't like it, don't watch it. This is political correctness rearing its ugly head again. Being offended doesn't mean you are right. You're offended? So what. Me too. We all are.
The one thing I've learned after years of writing professionally, blogging semi-professionally, and speaking publicly is that no matter what you say, someone will take offense. People today are overly sensitive, and there are some cranks out there who think that complaining is a valid way of contributing to discourse. They should be ignored.
I do not believe the BBC should avoid topics some viewers might find offensive because that can become a slippery slope. The world is full of people and almost every topic will offend someone in some way. I do not believe there is a sure fire way to eliminate topics that could offend without eliminating every topic there is.
Nothing that they say is going to offend someone to the point where they will be hurt much from it, and most likely a person offended will forget about it before the next day. So no they should not hold anything back, they can say whatever they think will get viewers.
There may still be fear of homosexuals, and animosity held against immigrants, or even the ongoing issues between Ireland and Britain. In order to alleviate the obviously sensitive social issues of modern time, it would be better not to address these on the BBC. However, nothing is completely politically correct. Even Dr. Who gets a little risque now and then. It adds to the drama as long as it is done in moderation and tastefully.