I took my oldest, who was 4 at the time, to see GEN (PG). He was already a TNG fan so I didn't think twice about bringing him along. The crash landing of the E-D was so loud in the theatre that it freaked him out. I kid him now that it had to be Shallaff's syndrome. I wanted to see it again but he didn't so my wife and I took him and my then 3-year-old daughter to a drive-in showing of it and told him my son that he could control the volume of the van's radio. He could turn it all the way down at the loud parts if he wanted. This worked out very well.
As they got older, in the 13-15 year range, we didn't allow them to see PG-13 films unless we saw it first. Way too much sex and nudity is allowed in movies with that rating. I've read that PG-13 means they can use the F-bomb once in the film. I must be getting old but I've seen too many PG-13 films that I felt should've been rated R.
I'm actually very happy to read what Pine said about this. While violence is often a part of the story, Trek really doesn't need foul language or sex scenes to make it exciting or realistic. It's always been about the stories, moral dilemas, and ethics for me.