I know they identify as Travellers, and not Gypsies, but I think the case of the grave of Willy Collins in Sheffield is an extreme example of what makes a lot of people shudder when it comes to people from a travelling culture.
The idea that they seem to be able to get away with whatever they like, assume that rules simply don't apply to them, the police and authorities are scared of them, and they just shout 'racism' when challenged on what the majority of people would see as widely unacceptable behaviour (whoever acted like that).
I realise that this by no means applies to all G/R/T people - but the events seem to happen on a regular enough basis that the instinct is to fear and distrust everybody from a travelling background.
Obviously not with the cemetery, but I think there is also the concern that, when people do travel around all the time, it's the perfect cover for the irresponsible ones who couldn't care less - when they themselves not only don't have to remain in communities that they leave in a mess but they are also harder to trace when they move on.
I'm also guessing that many travelling people genuinely see themselves as the victims of a vicious circle. If there aren't enough official sites for them where they need/want them, they have no choice but to invade parks and school playing fields. But these obviously have no facilities for the disposal of toilet and other household waste, so what else are they to do but leave it in the middle of the field - they are simply left with no alternative.
But because this is known to frequently happen, when there is talk of new official sites for Travellers or Gypsies, locals are fiercely against it - meaning that the respectful ones who just want a peaceful, law-abiding nomadic lifestyle, without leaving mess at all when they leave, are between a rock and a hard place.