I can't blame you; it's hard to respect someone who claims to be a follower of Jesus but doesn't act like it. Some of Jesus' harshest words were directed at hypocrites -- at people who claimed to follow God but denied it by the way they lived. Jesus said, "If you love me, keep my commands" (John 14:15).
Sadly, your neighbor may not even realize what she's doing. In fact, she may think she's a good Christian -- she's active in her church, lives a moral life, is concerned about others, and so forth. These things are important, of course; they'll be part of every sincere Christian's life. The Bible says, "Whatever happens, conduct yourselves in a manner worthy of the gospel of Christ" (Philippians 1:27).
But God doesn't only want to change our outward behavior -- important as that is. He also wants to change us from within, transforming our hearts and minds so we become more like Christ. I pray your neighbor will realize this, because only then will she want to speak truthfully and avoid hurting others by her words. The Bible says, "Each of you must put off falsehood and speak truthfully to your neighbor" (Ephesians 4:25).
Don't, however, let the inconsistent behavior of your neighbor keep you from Christ. He alone is perfect, and you can trust your life into His hands. God loves you, and Christ gave His life for you. By a simple prayer of faith you can commit your life to Him today.