This is an example of a legitimate no-solicitation rule. It confines the restriction to actual working times and places. See, Marathon LeTourneau Co. v. NLRB .
Rules attempting to restrict union distribution in break areas are improper.
A rally in the parking lot would be protected activity as long as the people participating are employees. Ten minutes before or after the shift would not be sufficient passage of time to cause the workers to be considered outsiders. The company could remove any outside organizers from the private property. The company cannot outlaw the wearing of union insignia, hats, etc. unless there is an overwhelming justification. If the button caused safety or other significant problems, the company could probably force its removal, but not if the removal is directed only against union buttons.