For the millionth time, this is not a free speech issue. The NFL is a business not the Government, The 1st amendment is protected speech from the Government. If you work for Macdonalds and start spewing your political bullshit to every customer that comes in, you'll be fired. The 1st doesn't protect you from that.
Last I heard, the President is indeed a part of the government. The government taking negative or punitive action because of your protected speech does indeed fall afoul of the first amendment. If this weren't the President, you might have a point. However, you do not.
This is not a positive or "active" punitive action. There have been no fines, no imprisonments, etc. They rescinded an invitation which by definition is technically inaction. They have no "right" to attend the White House.
If there had actually been punitive action taken against the players you might have a point. However, you do not.
If you act like you're not a patriot, you shouldn't be surprised when someone who fancies himself as a "supreme patriot" doesn't want anything to do with you.
On the other hand, this is punishment for free speech. And given that the government is not supposed to have any kind of an opinion or take any action against your free speech, this just kind of opened the door for some serious problems.