The right isn’t completely immune to this tactic. Back in 2005, some pro-life demonstrators outside Terri Schiavo’s hospice allowed (or, more likely, directed) their children to carry cups of water across police lines, where they were arrested. Sure, it was ludicrous--Terri Schiavo was unable to drink from a glass and relied on a feeding tube—but it accomplished several of the parents’ goals. First, it was an emotionally manipulative demonstration: supposedly naïve, innocent children just trying to deliver water to a disabled woman and getting handcuffed by thuggish cops. It also put the police in the impossible position of either allowing trespassing onto private property or arresting children. These parents sent their kids to do their dirty work for them. The parents weren't willing to be handcuffed and booked themselves, and they knew a prosecutor would never press charges against a kid. The children were literally their human shields.
It’s never okay. I’m not saying you shouldn’t impart your values to your child. I had a child seven weeks ago, and I consider it my duty to do so. But I won’t being using her as a proxy to convey my political beliefs. I’m a grown-up. I can do that myself—and so should anyone else who considers using “the children” to rig debates.