They allow teenagers at the venue. They must have a ticket but the exception to the rule I suppose is based on the event so check the event information to make sure it doesn't say otherwise. But, like I said, teenagers and even younger children are allowed to attend events at the Fillmore (accompanied by an adult of course). They usually hand out alcohol bands to those who are the required age for drinking and will not give the teens bands, incase you are also concerned about that.
I've seen children younger than 13 at The Fillmore.
The Fillmore is all ages. I took my 16 year old daughter to see a show there a couple weeks ago, it was really fun.
Always check and make sure all ages show Fillmore rules my favorite venue of San Francisco
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