I don't presume to dictate to others how they ought to feel about their own country. However I would not, whatever my view, ridicule others for feeling a sense of pride or showing respect for their own country, its institutions, its Head of State or for the national flag. To do so betrays a considerable lack of respect for the views and opinions of others - not to mention those of a large swathe of the population of the UK in this particular case.
I cannot begin to imagine that these two BBC presenters would have done that to an elected official representing the EU, or the USA or indeed Scotland. But it seems it is acceptable to belittle anyone who is proud of the British flag or our Monarch.
This has more than a touch of the Emily Thornberry about it. A disingenuous apology and un-liking a tweet really is not sufficient. The damage is done and it is not the first time these presenters have stepped over the line. If the BBC is serious about addressing concerns regarding bias, the first thing it ought to have done would be to remove these two, at least for a while. They are too full of themselves.