I had Samsungs secure wifi on while away in Thailand etc. It worked fine, had no affect on the use of the wifi. However, back in the UK, when secure wifi is 'protecting' me, the wifi doesn't work. I have to turn secure wifi off and then can browse fine.
So on public wifi you have to switch it off in order to use the wifi? Does it say anything? I know secure wifi routes it through secure servers in other countries which might slow it down. Also are you subscribed meaning unlimited protection?
Strange, I've had no issues with it. I usually connect to my works guest wifi and have no issues. Unless it's something to do with the public wifi you're connecting to.