That's always been the case though. Employees have always been able to, and of course should be able to, leave an organization because they don't like something management said or did. The threat of employees to leave, especially if they leave en masse, can of course influence management's behavior, but that's always been true.
What's different about today is that the political climate is such that employees are much more likely to leave because they disagree with management's political beliefs than they used to be. There's a hypersensitivity to it that didn't exist 15 or 20 years ago, and it seems to get even more sensitive by the day.
Neither the (far) left or the (far) right is immune to it - there are snowflakes on both sides. "You don't agree with me politically, which makes you a terrible person, so I don't want to be associated with you even in the most tangential or indirect way" is a motto that lots of people seem to live by right now.
Also, to your hypothetical about Jemele Hill, if that occurred it would receive nowhere near as much attention from the media as this Gundy situation did, and the attention it would receive would likely be from a critical bent (i.e., there'd be a lot of think pieces penned saying it was stupid for a player to leave of his coach's Jemele Hill t-shirt). Very very few, if any, media members would sympathize with that player, and quite a few would probably think he was stupid and overreacting. So I agree with you there.