There seems to be a stigma against not showing any magical powers. Neville's grandmother and uncle went to drastic means to get him to show some magical abilities. There also seems to be more tolerance towards Muggles than towards squibs themselves.
The attitude of the wizarding population towards Squibs isn't uniform, just as it isn't towards Muggles or Muggle-borns. Some people look down on them. Others do not.
Attitudes towards Squibs include contempt...
It had always been the proud boast of Mr Buchanan senior that such an anomaly had never occurred in their family. The proud old warlock went further: a Squib in any family was a sign that they were in decline and deserved to be winnowed out.
(Pottermore, "Scottish Rugby").
"You disgusting little Squib, you filthy blood traitor!" roared Gaunt, losing control, and his hands closed around his daughter's throat.
(Half-Blood Prince, Chapter 10, The House of Gaunt).
"I'm a Squib," said Mrs Figg. "So you wouldn't have me registered, would you?"
"A Squib, eh?" said Fudge, eyeing her suspiciously. "We'll be checking that. You'll leave details of your parentage with my assistant Weasley."
(Order of the Phoenix, Chapter 8, The Hearing).
"And what difference does that make?" asked Filch obnoxiously.
"I'm a ruddy teacher, aren' I, yeh sneakin' Squib!" said Hagrid, firing up at once.
(Half-Blood Prince, Chapter 19, Elf Tails).
"And what on earth's a Squib?" said Harry.
To his surprise, Ron stifled a snigger.
"Well - it's not funny really - but as it's Filch..." he said. "A Squib is someone who was born into a wizarding family but hasn't got any magic powers. Kind of the opposite of Muggle-born wizards, but Squibs are quite unusual. If Filch's trying to learn magic from a Kwikspell course, I reckon he must be a Squib. It would explain a lot. Like why he hates students so much." Ron gave a satisfied smile. "He's bitter."
(Chamber of Secrets, Chapter 9, The Writing on the Wall).
Note that Hagrid and Ron wouldn't ordinarily take satisfaction in mocking a Squib. They do so on this occasion because this particular Squib is a bully.
So there are a variety of views. Those most likely to look down on Muggles would similarly look down on Squibs because they believe themselves to be superior to those without magic. Similarly, those who are kind and accepting towards Muggle-borns are most likely to be sympathetic towards Squibs. Squibs are not necessarily viewed less favourably than Muggles. It all depends on who you're talking to.
The attitude of wizarding society as a whole towards Squibs used to be very hostile in days gone by, when Squibs certainly were treated as second-class citizens, to the extent of being kept a secret and removed from society.
"In our day Squibs were often hushed up. Though to take it to the extreme of actually imprisoning a little girl in the house and pretending she didn't exist -"
"I tell you, that's not what happened!" said Doge, but Auntie Muriel steamrollered on, still addressing Harry.
"Squibs were usually shipped off to Muggle schools and encouraged to integrate into the Muggle community...much kinder than trying to find them a place in the wizarding world, where they must always be second class..."
(Deathly Hallows, Chapter 8, The Wedding).
Indeed, public opinion was almost universally negative until 1900, when Angus Buchanan brought out an revelatory personal account of his experiences as a Squib. This brought about more sympathy and understanding towards Squibs.
Reunion with his family caused Angus to reevaluate his relationship with his magical roots and in 1900 he published the groundbreaking worldwide bestseller My Life As A Squib. Until this point, Squibs had lived in the shadows. Some clung to the fringes of the wizarding world, always feeling second-class and trying to fit in; others cut all ties and lived entirely as Muggles, often repudiating their beginnings. My Life As A Squib brought the plight of these individuals to the wizarding world’s attention.
(Pottermore, "Scottish Rugby").
Nevertheless, the desperate attempts that Filch made to keep his Squib status a secret when Harry discovered his Kwikspell letter shows that there was a fair amount of stigma and prejudice about even in more modern times.
"Have you - did you read -?" he spluttered.
"No," Harry lied quickly.
Filch's knobbly hands were twisting together.
"If I thought you'd read my private...not that it's mine...for a friend...be that as it may...however..."
Harry was staring at him, alarmed; Filch had never looked madder. His eyes were popping, a tic was going in one of his pouchy cheeks and the tartan scarf didn't help.
"Very well...go...and don't breathe a word..."
(Chamber of Secrets, Chapter 8, The Deathday Party).
We don't usually see Muggle-borns trying to cover up their identity like Filch does here. Usually Muggle-borns are treated with respect, with the exception of an extreme core of blood purists, so there's no need to hide their blood status (this wasn't true during Voldemort's reign of terror in Deathly Hallows, but that was an exceptional period of wizarding history). One could argue that the way in which Squibs seem to be more shy than Muggle-borns about their identity shows that they are held in worse esteem by society as a whole. However, this is probably tied up in the tendency of Squibs (well, certainly ones like Filch) to see their own Squib-ness as intrinsically embarrassing. Generally speaking, those who are inclined to look down on Squibs would look down on Muggles and Muggle-borns as well, and not reserve any special scorn for Squibs. If anything, Squibs may be viewed more favourably than Muggle-borns by blood purists because of their magical heritage.
The behaviour of Neville's family is particular to them. They show a stifling expectation of great things from Neville throughout the series. They're always hoping for great things from Neville so that he would live up to the great example of his all-star Auror parents, Frank and Alice. He had that pressure on him even when he wasn't demonstrating any tangible signs of magic. His family weren't necessarily anti-Squib. They just didn't want Neville to be a disappointment.
This question is like asking:
Why do people mock disabled people?
It works very well as a proxy for learning difficulties or physical disabilities. This is a common trope in the fantasy genre; talking about issues we face as a society by putting them in the context of another society. Other examples in Harry Potter include:
The Squibs are looked down on more than muggle-borns because they are born into the wizarding world, and just like belonging to any community this comes with certain privileges and expectations. The main expectation of any member of the wizard society is to be able to perform magic. It's seen as shameful that wizard parents would produce non-wizard children.
Bear in mind that a lot of the harsher reactions to squibs are a generation or two before Harry and his friends. Often the further back in time we look, the worse folks who fail to meet these expectations have it.
Consider, for instance, illiteracy. In parts of the world with universal education, it's shameful to be illiterate. They'd be looked down on. In places with a less developed education system, nobody would expect that everyone can read and write (or read and write well), so there's no shame attached to missing that expectation.
Squibs are, through no fault of their own, sidelined by the society they're born into because they are lacking a capability which magically-capable wizards are all expected to have, and take for granted.
Couldn't that be like folks born with a missing limb? Those who can't read? Speak clearly? Who can't see, hear or speak as well as expected? How about those who can't support their families? Who are trapped in addiction? There's countless reasons folks are ostracised which bear resemblance to
By talking about this in a different context, J.K. is talking about societal problems in the real world without tackling it directly, where many readers would respond to it with their preconceived ideas about people who are disabled, homeless, etc.