How old is the child? Under 18 or over 18?
I wouldn't kick a child under the age of 18 out of the house under any circumstances short of them being literally violent.
If the child is an adult child, capable of making their own way in life, then if they disrupt the household enough then they might have to find a new home until they can chill out.
If I had a child, I'd try to raise her to be reasonable and compassionate, and I would give her exposure to the beliefs and cultures of the world, so I would find it very unlikely that she would end up with malevolent and narrow-minded beliefs. But people should be free to follow where their thoughts lead. If the child turns down a path that I find ridiculous, I'll make my disappointment known and try to be a better example to turn them back.
I think these are certainly important distinctions, and perhaps tweaks a few answers here.
Under 18, my children are my sole responsibility for their protection, education, and welfare. Short of them being threatening to our safety, I would never kick them out.
After 18, however, my husband and I fully expect our children to have the ability to live on their own if they've graduated high school. And converting to another religion, depending on the obligations they might feel they have toward their congregation or faith, might create more static in the household than if they were living on their own.
How we've raised our kids, it hasn't been any issue at all for us. Our oldest 2 are independent - one is transitioning out and one has done so already - and neither gave any disruptions in spite of varying beliefs from us. But if they do consider it during the time of transitioning out to their own, we're very comfortable talking about what boundaries we all will want from each other, and what bridges we wish to build/strengthen.
But yeah, if one of our other teenaged kids (aged 14 and 15 at the moment) were to convert and begin preaching, we take most things from our teens with a healthy grain of salt anyway. They're establishing their identity, and finding themselves, and beginning to rebel in ways that help them feel comfortable with breaking away from us as their parents. Hubbie and I would probably let them preach a bit to get it out of their system, and then ask if they want macaroni and cheese for dinner or if they're all right with a casserole dish.