If her cat is outside roaming it's at a lot more risk from cars, feral cats, dogs, wild critters than it is from your securely enclosed in your own home ball python.
Having said that people have phobias, way more than just fear and not at all rationally based. I will happily, with help, wrangle our almost 9 foot boa constrictor but I have a deep seated gawd awful fear of stupid june bugs. Yep june bugs! How dumb is that but they literally make my skin crawl, I'm convinced they all want to buzz into my long hair and I feel like throwing up if one is outside buzzing around my porch light. I can't even stay outside if one is there. That's a phobia, way more than simple fear and pretty much something I'm unlikely to get over. Rationally I know june bugs do NOT have it in for me and can do me no harm but instinctually I dread them.
If your neighbour has a phobia about snakes, do what you can but understand she can't really control it. Educating her may help but not always. Do what you can, be understanding, informative but also kind. Not everyone has to like snakes just because we do.
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