Yes, it could affect you.
If your neighbor is actually cognizant of spiritual warfare, and not just mouthing the blabberings of television evangelists about being a “soldier for Jesus,” then there is every chance he will be able to sense any spirits you call, and work against you.
EA tells a story in his book “Baneful Magick” where he describes working for a man who was a Christian and talked about freeing witches from demons and so forth, and EA decided to test astral weapons against him because he didn’t think the guy was actually spiritually aware, but not only was the guy aware of the attack, he knew EA was the one who sent it.
My advice would be to set up wards in your working area so any spiritual energies are confined to your space, and a daily banishing ritual to prevent any energetic buildup that could cause problems. I also suggest you shield yourself so the owner will not sense any demonic energies you may call upon.