The Robertsons don’t have to break the contract A&E will.
All the Robertson’s have to do is ... nothing.
If A&E just wants to film them doing nothing with Phil constantly there :) then they are welcome too. A&E can’t force the Robertsons to do ANYTHING funny or entertaining. So if A&E wants to have a season 5 of just watching them make duck calls without saying a word, then let them.
They should just give plenty of interviews in which they state the same thing regarding homosexuality that Phil did. A&E would either have to admit their mistake or let the whole family go.