I'd be remiss not to start with a quote from Good Subjective, Bad Subjective:
Parenting is one of the most subjective subjects I can imagine; every child is different, every parent is different, and whole cultures are wildly different in how they approach child rearing.
The entire post is worth reading as is the original Back It Up! principle. But the Reader's Digest version is that good answers are more than the author's personal opinion. The potential difficulty with quoting Scripture is that it adds authority from your perspective and does nothing for readers who don't accept the Bible as gospel (so to speak).
Parents are bombarded with conflicting advice. Most of it is well-intentioned. But it's just not very useful. To quote from a post on Meta Islam:
Being correct is not the same as being useful.
In my opinion, the goal of a Q&A site about parenting isn't so much to have a bunch of correct answers as to have answers that are useful for helping parents raise their children. Given the wide range of experiences and circumstances, that's an exceedingly difficult thing to do in the best of circumstances. It's certainly not going to work to cite the Bible as an authority when many parents don't accept it as authoritative.
Even so, I think there are ways to bring religious texts into a post in a way that is useful. An obvious situation is when askers themselves use the Bible as an authority. Less obvious is when the religious text played a part in "experiences that happened to you personally". For instance:
When my oldest son was in elementary school, he often got frustrated with my jokes and teasing while we walked to school. I figured it didn't hurt since my own father used to do the same thing with me. But then I read:
Fathers, do not provoke your children to anger, but bring them up in the discipline and instruction of the Lord.—Ephesians 6:4 (ESV)
After thinking about that verse, I remembered how my dad would catch himself in the middle of horseplay and get serious. He must have noticed I wasn't having fun anymore, so he'd stop well before I got angry with him. I realized I was being selfish and that I needed to treat my son the way I'd like to be treated.
So I started using the walk to school to find out what sorts of things he was interested in, which gave me tons of parenting opportunities. We didn't stop having fun, but I stopped pushing my teasing to the limit of his patience.
Notice that it really doesn't matter whether you trust the Bible verse to be reliable. The important bit is that the verse changed the way I approached my job as parent. It's entirely possible I misinterpreted the verse, but that's not really a problem because the verse was useful in helping me fix the way I interact with my son. For the right question, my story could be helpful to any reader who interacts with children.
Just as important, you can immediately identify whether the advice fits into your parenting style or philosophy. If, by chance, you pattern yourself on George Bluth, you can skip this advice altogether.
Finally, I should note that if you always quote the Bible, your posts might be seen as propaganda. To paraphrase the help center:
If a large percentage of your posts include a mention of your [religious convictions], you're probably here for the wrong reasons.
The same would be true if every post mentioned, say, The Bradley Method® or a specific scientific study or anything that a person might be promoting.