A sizeable percentage of the wizarding world are either half-bloods or Muggle-born, which means that much of the wizarding world has at least two Muggle grandparents. It also means that a substantial percentage are married to Muggles. I can't say how many because half-blood seems to mean "half pureblood," not "half-Muggle." I suspect that most half-bloods are the children of Muggle-borns, not Muggles, just because wizards don't mix with Muggles that often. Anyway, this produces a problem - wizards need or feel the need to remain secret from the Muggle world, but and at the same time, they have members of Muggle families right there with them. How does the wizarding world manage this contradiction? This essay will address the problems and the possible solutions.
We know that wizards have laws mandating secrecy, with whole government divisions dedicated to preserving this. We can even figure out why this would be so. The Founders established Hogwarts at a time when it was getting dangerous to be open about magic (so says Flitwick) and we know that there were witch hunts in last few centuries in Europe. While I don't believe in the "Burning Times", there is no doubt that thousands of people, largely old, female and outcast (and probably nonmagical even in Rowlings universe, and also probably the dominant religion, but that's immaterial) were killed as witches.
Were true wizards also killed? Depends if they had their wands on them, and could get away, like the rather fabulous Wenelda the Weird, with casting spells that would not harm them. Because I'd think the probable response to that would be something less than humorous and more deadly, unless Wenelda also had an invisibility cloak. On the other hand, they are more resiliant than Muggles, so we just don't know.
There have also been periods of time when witches were hunted more assudiously than others. In Britain, in recent history, there would be the reign of James I, who was historically paranoid about witches, and the Puritan regime under Cromwell. (I suspect that there were few Roundhead wizards, too.) All of this would only reinforce the need to keep underground even during less oppressive times, such as our own.
And yet, a full quarter of wizards come from Muggle families, and another quarter come from mixed ones. Plus, as we well know, Muggle governments know all about the Wizarding world, and how do you keep that lot totally silent? They have to do something, and Memory Charms have their limits.
And let's not forget the potential problems from the other side. In one of the rpgs I follow, among the other jobs that McGonagall has is fostering Muggle-born students who have been abandoned by their families (often taking the form of not meeting them at King's Cross.) This seems horribly plausible. Yet, none of the Muggle-born students we know in canon seem to have that problem. They keep in contact with their families and go home for Christmas (no one seems to go home for Easter.) And you'd think that Muggle spouses and their families would also be a major problem - even more, Muggle *former* spouses.
But there are solutions. These are dependent on wizards charming Muggles without permission, but that's perfectly canonical, if less than ethical - way less than ethical.
For the Muggle-borns, there are two problems. One is parental acceptance, whether it's because their ambitions for their children (Eton, for example, or whatever brilliant career Hermione would have had)would not happen or because magic is...weird. In other eras/places, "witchcraft" as sin might also be factor, although I doubt it for contemporary Britain. Contemporary US, on the other hand, is something else. There might also be exploitation of the child's abilities, but the laws against Underage Magic would protect against that. (And that might be the real reason behind those laws. Huh.) The other would be secrecy. One gossipy parent could hurt everyone, if that parent were believed - and there were and are times and places where that parent would be believed.
I propose that the families of Muggle-borns are placed under two different spells, both quite against their knowledge. The one would force them to *accept* the children as they are, so they would continue to care for them and not condemn them for their magic. They might even make them think it's wonderful, but that might be too much against true antipathy, and more than is necessary. Those families that *do* think it's wonderful would be charmed to keep that attitude, though. The other would prevent them from speaking about this around Muggles or others so spelled. They might even be charmed to not speak about magic at all - notice how difficult it is for the Dursleys to speak about it. Part is their natural antipathy, I'm sure, but I wonder if there's also a magical component.
They may even be given a believable cover story. "Justin? He's at St. Helga's, a very exclusive school for gifted children in Scotland." "Oh, Hermione is a prefect at St. Godric's. We're so proud of her." "That boy? St. Brutus'. It's just what he needs to straighten him out." Okay, Vernon could come up with that one on his own. An especially recalcitrant parent might even think the cover story is true.
This would also work for the government contacts. It would prevent them talking to their own families or anyone else about the wizarding world while permitting the wizarding world to feel safe about dealing with them.
It would be slightly more complicated for Muggle spouses. I'd think the wizarding partner would be given a choice, or seem to be. Choice one would be for the wizarding partner to not say anything to the spouse or inlaws. The wizarding partner would have to live as a Muggle, of course - they might even be monitored like underage wizards. This has several drawbacks - someone raised as a wizard would have difficulty adjusting to living without magic and may well be unemployable, for example. Another potential problem is children - there seems to be a good chance that at least one child will be magical. At this point, the secret is out - and that will put a major strain on the marriage. Witness the Finnegans.
The other solution is to treat the spouse and inlaws like Muggleborn parents - accepting the wizard's magic (and that of potential children) and not talking about it. Again, this would be up to the wizard, not the Muggles, officially.
I think this would solve a multitude of problems, explain things such as Lily's parents complete acceptance of her (Petunia, who is only a sister, would only get the geas against talking, since she couldn't abandon her sister, and seem sufficient for her to keep Harry.) and the government's compliance with the secrecy act. And the highhandedness is completely within the normal wizarding attitude towards Muggles.
Edited because I can't cite where I saw real numbers.