I don't at all see where some of these places get 13 as a good age of consent for many things. It's odd that 13 even comes up. I know that in Jewish custom, for example, 13 is considered the age of adulthood. Are there any other customs that do so?
Personally, I don't buy it; 13 is the age of introducing some responsibility. It's still definitely within the realm of impressionability and still too early in life to burden someone down with so much personal and social responsibility. Getting someone "out of naïveté" is a longer process than just one birthday, especially so young.
18 is the standard age which should be the legal age the world over, not subject to culture or religion. It is the law in many countries and if someone is under that age, they are minors; above it, they are adults, neither minors nor "teens". There's no such thing as a "teen adult", something the newsmedia loves to occasionally nudge us with in their 'news articles'. No. They have no license to grey it like that, First Amendment or not.
On another, less-seen and drastic hand, I've seen many religious families who, when their kids turn 18, conclude the birthday party, clear the table, hand their newly-18 kid their belongings in bags and tell them "You're an adult now. Gitchyersh** an' GTFO". Kicked the kids out of the house, even still enrolled in high school. On "religious grounds". Loser parents...just because the state draws a line doesn't mean they must do it, too. But they did...
Almost 30 years later, the internet remains one of the biggest Pandora's Boxes and social experiments in world history. Another venue of half-measures and mixed blessings. Surf wisely, folks; we've got constant gale conditions and they gave us flimsy boards.