Politely, you don't know enough about furries. Let me give you some details:
The fandom has a substantial sexual wing. This is not a moral judgement, just a fact. Survey data of thousands of furries finds a large minority describing sexual attraction as important to their furry activities, with many others acknowledging at least some sexual interest. That is why the scene has its own vocabulary for porn and why so many events have to manage adult content. 
Because organisers know this, big cons put in strict controls to keep adult material away from minors. That is unusual outside spaces where sexual content is expected, and it is telling. For example, Midwest FurFest explicitly instructs dealers to keep adult materials out of sight and reach of anyone under 18, with clear marking of minor badges. You do not need rules like that for a hobby that is purely “cute dress up”.
There have been serious incidents. RainFurrest 2016 was cancelled after the host hotel pulled out, citing years of damage and 2015 reports that included police visits, vandalism and arrests for assault and sexual assault. That is not “someone being a berk in a costume”, it is a pattern of problems that made a major venue walk away.
Another convention in Denver was also cancelled amid controversies that included allegations around organisers and attendees, which underlines that the scene can attract the sort of issues that make venues and cities nervous. 
Public versus private matters. You are right that UK law does not criminalise mere nudity by itself, but it very clearly draws a line at behaviour that causes harassment, alarm or distress, or crosses into indecency. The test in family spaces is not “is it technically illegal”, it is “is it appropriate to impose a sexualised subculture on a captive audience, including children”.
With fursuiting, outsiders cannot tell who is in the non-sexual minority and who is using the costume as part of a sexual persona. Full masking and anonymity are known features for many who do sexual role-play in these costumes. If you would not wear BDSM gear on a commuter train because others have not consented to being part of your scene, the same courtesy should apply here. The combination of anonymity, animal play aesthetics and a documented sexual subculture is exactly why people object in public, child-heavy settings.
No one is saying adults cannot do what they like in private venues, 18-plus hotel floors, or properly stewarded events. But pretending this is just “harmless fancy dress” in front of kids and in public ignores the reality that a significant slice of the fandom is sexual, that cons treat it as such with adult-content controls, and that there have been enough serious incidents to justify caution. Keep it to age-gated spaces and away from captive audiences on trains and in family areas. That is a reasonable boundary..
I sound like a stuck record but just like no males in female spaces, no masked fetishisits in public :)