I do not shop there, but so far I have read nothing that would make me stop if I did. A vet had an issues with a civilian employee wearing a uniform, I agree with the vet, but we have no idea why he was asked my management to leave or have to be escorted out and banned.
Old Navy corporate released a statement backing military, so I am not sure of the reason why anyone would boycott the store. It seems like a single incident without enough information to even make a judgement one way or the other.
disclaimer: This statement is completely based on the short article posted. Video did not work.