So having taken my kids forever it is more a suggestion. My kids have never been turned away. But I will say if you are signing up your kids and they are younger than the age posted you need to make sure your kids being there aren't ruining the event someone else is paying money to participate in. Also they need to be able to play the event independent of your being there. Basically you shouldn't be coaching them.
Easiest example on the first point is True Dungeon. It is labeled age 13+ and your kids should really be 13+ to do it since everyone in that room is paying $88 to do it. While your 8 year is likely capable to slide a puck at the target. They won't necessarily get out of the way, focus on the task at hand or not muck up other's experience in some way. You will have 8 other angry people in the room with you. I have seen this multiple times.
You may be alright in Warhammer provided your kid is independent enough with others. Since most warhammer is tournaments and they are going to potentially get paired up with a stranger and the stranger doesn't want to be babysitting your kid. They need to be fine without you by their side.
All that being said I have signed up daughter up for a ton of board games at Gencon and never had a problem. But I knew she wouldn't take away from anyone else because she plays fast, plays independently and has no problem understanding rules. So she was always like any other adult they might play against.