If A&E wants to succumb to Right Wing reactionaryism so be it, that is their choice. So like the Flush Rush Movement, Dump the Duck movement should commence. But do it where it really hurts.
A & E Channel is part of a global A & E Network partnership between the Hearst Corporation (Hearst Trust) and Disney-ABC Television Group. They are big but they are vulnerable just like Clear Channel radio is vulnerable.
Start with the actual cable providers. Comcast and what not. Many providers are licensed in local municipalities which if there is an offensive programming broadcast that channel can be removed or moved to the pay or premium channels lineup. This can be done on a national basis too, or at least move it out of basic cable lineup as A & E reports that it is in 96M households and on 86% of cable lineups.
Then move to specific advertisers, if Duck is the number one rated A & E Show than they are selling ad space nationally specifically for that spot, either through the cable provider or some partnership. Identify the ad sponsors and Flush them out.
Next move to start boycotting specific offerings of the Hearst and Disney/ABC. Hearst owns a ton of magazines from Cosmo to Oprah, even better one of the heirs still own the Albany newspaper and the SF Chronicle and Houston Chronicle.
ABC and Disney have many pressure points as well, simply boycotting the theme parks or turning away from their national news would be a good start. Again they have advertisers and if a concentrated effort was made to their advertisers that 2/3's of the nation who are against bigotry will not patronize your product offerings because you advertise your wares on a network that endorses a bigot cable bit performer it has its effect.
Not sure how the Flush Rush campaign got started or coordinated but maybe I can strike a match.