Here's what the 2017 official NFL rulebook says.
As for being on the field ahead of the start of the game, there's no mention of the national anthem or requirement to stand for it. There is a requirement for teams to be on the field 10 minutes prior to the kickoff. That means teams that stayed in the locker room Sunday, typically had ample time to make their way to the field.
“SECTION 2 STARTING A PERIOD OR HALF
ARTICLE 1. KICKOFF ON SCHEDULE. Both teams must be on the field to kick off at the scheduled time for the start of each half. Prior to the start of the game, both teams are required to appear on the field at least 10 minutes prior to the scheduled kickoff in order to ensure sufficient time for proper warm-up. Designated members of the officiating crew must notify both head coaches personally of the scheduled time for kickoff prior to the start of each half."
Here is the only real policy on political statements and NFL standards, via the official rulebook.
“SECTION 4 EQUIPMENT, UNIFORMS, PLAYER APPEARANCE
ARTICLE 8. PERSONAL MESSAGES. Throughout the period on game-day that a player is visible to the stadium and television audience (including in pregame warm-ups, in the bench area, and during postgame interviews in the locker room or on the field), players are prohibited from wearing, displaying, or otherwise conveying personal messages either in writing or illustration, unless such message has been approved in advance by the League office. Items to celebrate anniversaries or memorable events, or to honor or commemorate individuals, such as helmet decals, and arm bands and jersey patches on players' uniforms, are prohibited unless approved in advance by the League office. All such items approved by the League office, if any, must relate to team or League events or personages. The League will not grant permission for any club or player to wear, display, or otherwise convey messages, through helmet decals, arm bands, jersey patches, or other items affixed to game uniforms or equipment, which relate to political activities or causes, other non-football events, causes or campaigns, or charitable causes or campaigns. Further, any such approved items must be modest in size, tasteful, non-commercial, and non- controversial; must not be worn for more than one football season; and if approved for use by a specific team, must not be worn by players on other teams in the League."
So that means the players who wore “I’m with Kap” shirts could have broken NFL rules if the league did not approve them ahead of time.
The league could have also taken action at kneeling during the anthem as a form of protest if it deemed it conveying a personal message through illustration. It's quite clear that the NFL won't do so at this time.