Tom Ascol has some helpful thoughts (here and here) on Paul's principle of accommodation in 1 Corinthians 9.
Here are a couple of good distinctions he makes:
"I would make a sharp distinction between compromising what God has revealed in His Word and accommodating others where we can for the sake of gaining a hearing for the Gospel."
"It is vitally important to distinguish between the essence of our liberty before God, and the exercise of that liberty before men. There is an important difference between Christian liberty and the use of Christian liberty."
