In this interview with John MacArthur and related article, he discusses when to leave a church.  Three points in his commentary are helpful when thinking about this topic:

1) You don’t go to church, you are the church. You take the church to the place.
2) Don’t be in a big hurry to leave unless you know that the Word of God is being compromised either in the teaching, or in the living of the leadership… But the question that needs to be asked is is he faithful to the core of the gospel (Triune God, deity of Christ, deity of the Holy Spirit, deity of God the Father, the virgin birth, the sinless life of Christ, substitutionary atonement, literal resurrection, salvation by grace alone through faith alone in Christ alone)? That’s what I call the drive train. If those things are right, you might have to tolerate some of the other things that aren’t nearly as absolutely critical as those are
3) Many Christians in history not having the option to select a church. It’s more of an American consumer mentality (my paraphrase)

Based on MacArthur’s thoughts as background context, here are eight questions to consider as you think about the decision to stay or leave:

1) Can you continue to wholeheartedly support the mission and ministry of your current church with your time, talents and treasures?  Are the issues new or long-lasting?
2) Are the theology issues major or minor?  How sure are you of your view?
3) Are your children impacted in a negative way or would they be better off elsewhere?
4) Are you and/or your spouse significantly impacted in a negative way or would you be better off elsewhere?
5) The grass may not be greener elsewhere and not attending isn’t an option (Hebrews 10:25), so do you know of a good alternative?
6) How much are you damaging the church (i.e., the people) by leaving (Mark 12:31)?
7) Can you influence the reformation of the church by staying?
8) How is God most glorified (1 Corinthians 10:31)?
9) Have you searched your heart to make sure that the issue isn’t with you (Jeremiah 17:9)?

If, after careful consideration and prayer, you decide to leave here are questions to ask of a new church.