IIRC, "NFL Enterprises L.P., is a limited partnership constituted under the laws of the State of Delaware. It is a separate and distinct entity from the National Football League which is an unincorporated, not for profit association, constituted under the laws of the State of New York. The NFL is a joint enterprise of thirty member clubs distributed throughout the United States which are engaged in the business of exhibiting football games."
As such the owners make up the rules and they do not want your cause plastered on their uniforms they just want to play football and make tons of money in that and related activities.