There is a nice lady that lives next door to me in the neighborhood I just moved into with my family. One day recently I decided to try talking to her about Jesus. I was shocked at how quickly she turned hostile. She made it clear she believes in God, but she expressed resentment and hatred for him. She said that her mother had been religious, but her stepfather had driven her to suicide several years ago. She told me that she cannot accept a God that allowed her mother to suffer at the hands of such a wicked man. My neighbor then stormed off angry at me for even bringing God up in conversation. Since that day, I've noticed out the window her talking to other neighbors, and heads turn in the direction of our house. I'm worried that since we're new here, we may end up outcasts before we get a chance to prove ourselves good neighbors. Is the next step an apology? I don't think I said anything wrong, but I'm willing to take the higher road if necessary.
Your neighbors response is not that unusual. People will adhere to all kinds of reasons to turn their backs on God. Perhaps she feels she has legitimate reasons to despise God, or perhaps she uses it as an excuse to dislike God's people.
Jesus made it sound easy when He told the disciples: Mat 10:14 "Whoever does not receive you, nor heed your words, as you go out of that house or that city, shake the dust off your feet." However, when it is your next door neighbor, it's not so easy.
Even though it sounds as if you didn't say or do anything wrong, I agree with your idea to approach her with an apology. I would only express remorse for upsetting her, but remain silent on the issue of bringing up the Lord. I would never encourage anyone to apologize for that! In that regard your were obeying God.
Since this is someone you may live next door to for years to come, it wouldn't hurt to bring a peace offering such as cookies, or invite her in for lunch. In this way you rise up above any hostility.
Pro 25:21-22 If your enemy is hungry, give him food to eat;I would perhaps do your best to show kindness to your other neighbors when opportunity arises.
And if he is thirsty, give him water to drink;
For you will heap burning coals on his head,
And the LORD will reward you.
Mat 5:16 "Let your light shine before men in such a way that they may see your good works, and glorify your Father who is in heaven.Most of all, continue to pray for them.