Thing is with this whole problem, there is no solution without discriminating against somebody. On one hand, you can't possibly have big burly blokes at the gates of a family theme park charged with making decisions of a social cleansing type nature. It's also wrong for a company to make public generalisations to its potential customers by labelling these days publicly as "traveller day" as a warning to others and it's my firm belief, especially in the current political climate, that such things can actually make the problem worse in the long run (although I would strongly defend every individuals right to do so in a free country as long as we're talking about facts).
On the other hand, it's downright unfair to expect unaware customers, particularly families with small children to have to experience this kind of thing when all they did was turn up for a good day out. If you plan and pay for a trip to Towers, you have every right to expect a safe and friendly day out with your family. You shouldn't have to trawl through fan forums and search the Internet high and low to "research" what days are safe for you to visit or not.
The park is private property at the end of the day and there must be a better solution than the current one of just bracing themselves for the worst. But the solution is probably far more complex than much of what has been already discussed in this thread.
The argument of "we just have to put up with it", as if abusive hooligans should be allowed to run around abusing and intimidating people and causing criminal damage on PRIVATE property is something to be tolerated is just as moronic as the argument for "a pikey ban", whatever that's supposed to mean.