As someone who is bi, I am completely supportive. My own grandparents had a handful when I came out at age 15. Love is love, and it's not gender based. People can end up in any situation. Being lesbian, gay, bi, or transgender is not a choice but a circumstance. The hardest part of being a parent is accepting that and trying not to find "blame" anywhere.
Tell the person to just love and be herself or himself, and never be judgmental or narrow-minded. I would also mention some great role models who are lesbian or gay, and say "look at what they are doing... you can be anything you want." Don't let your kids feel like victims, or allow them to become too dependent on certain parental behaviors. Children are only indoor plants up to a certain age, and then they can grow outside in the "elements" when ready. Don't molly coddle them.
There does not have to be obstacles. However the best part of being a parent is to be the safety net for that child if something happens, and to always be there to protect and look out for her or him, from a distance. Also give kids the chance to make mistakes and learn themselves.
When a person comes out, there is a lot of confusion and uncertainty. Adding to that confusion with one's own ignorance not good parenting. Parents have to look beyond how they might look in the world or their sphere of intimates if they feel singled out, embarrassed or ostracized. I know it is hard for a parent to put a child first. It's much easier to just tell the child to just "fit in". But that is really a crock. Loving caring parents don't abandon their child. And they should not dismiss them, or else they risk being "dismissed" themselves as parents.
Remember that parents can shoulder some of that pressure. Parents worry about the rest of the family and neighbors, and that is understandable. But soon as a parent takes a stand in favor of and supporting their child, watch more people move to your side of things.
People avoid conflict and most kinds of unbalancing "elements". But people are not simple. We are not robots or linear beings who accept whatever crap gets shoved down our throat. That was so last century.
I should also point out that age of consent stuff is important and kids who come out need a bit of extra advice on this. Sorry for mentioning. Kids really do need love and guidance from parents and family. And perhaps not all parents know this stuff and they also need guidance. Don't expect parents to know everything.