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 They rescinded an invitation which by definition is technically inaction.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 the White House cannot block twitter users (by your definition, a non-negative, non-punitive action), then oughtn't the same standards be applied?
You also don't have a right to have a Twitter account but the White House can't block twitter users.
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.