Were it not for the fact that he's Leader of HM's Loyal Opposition, I'd have some sympathy for Corbyn. I'm no republican, and dour as it sounds I will always stand for/ join in the National Anthem. But I remember feeling incredibly awkward as a child when, say, at church or in the Scouts, prayers were said and religious songs would be sung. Being no longer religious at the point, joining in felt hypocritical even, let alone awkward, especially in the prayers. So I would refuse to join in -- not meant as a statement of my contempt, but out of respect for those who were participating. I don't know if it came across that way or not but I'd have sympathy with anyone not wanting to join in to something they disagreed with, meant as a statement or not.
But I am/ was a child nobody cared about particularly, whereas Corbyn is the leader of a party with ambitions to serve as HM's government, and not singing under the glare of TV cameras and the media. A refusal to join in, even if meant for honorable reasons, is bound to come across the wrong way, and he must be far more careful in future to show respect where it is due. I'm not convinced he will, though.