A public house is a house open to the public - there still may be rules to follow, and indeed few people question the age limit. A "free" house is one not tied to a particluar brewery, it's not a reflection on it's door policy or beer prices!
Look at it from the publican's point of view: if (say) a gang in town, known for random violence/bad behaviour/general lawlessness took to wearing top hats, tails and monocles, it would be a sensible precaution to ban such attire from his establishment.