To clarify, this is different from the question How involved are Muggle parents in the school lives of their magical kids? I am not talking about coming to Hogwarts. I am thinking outside the school. We know they can go to Diagon Alley with their kids, but could they go alone? Could they visit Hogsmeade? Could they get a job in the wizarding world? We know Squibs can, like Filch. Are there laws on the subject?
There are practical considerations, but no known laws in Britain.
There’s no mention of any laws (in Britain) on whether Muggles who are allowed to know about the wizarding world can visit wizarding places alone or if they can hold jobs in the magical world. There are no known cases of either, however, and there are practical reasons why it would be difficult.
It’s unclear how many wizarding places let Muggles visit alone.
We know that Muggle parents (and presumably Muggles who marry wizards) are allowed to visit places like Platform Nine and Three-Quarters and Diagon Alley while with their wizard relation. However, it’s not mentioned whether they could visit alone, since they’d already know of magic so it wouldn’t be breaking the Statute of Secrecy. It’s unclear if Muggles can visit Hogsmeade, even with their wizard family member. In addition, some wizarding places are invisible to Muggles, like the Leaky Cauldron - which would make visiting alone difficult, even if it’s allowed.
“Dumbledore handed Riddle the envelope containing his list of equipment, and, after telling Riddle exactly how to get to the Leaky Cauldron from the orphanage, he said, ‘You will be able to see it, although Muggles around you – non-magical people, that is – will not. Ask for Tom the barman – easy enough to remember, as he shares your name –”
- Harry Potter and the Half-Blood Prince, Chapter 13 (The Secret Riddle)
If they couldn’t see the entrance to the Leaky Cauldron, then it’d make getting in to it and by extension Diagon Alley as a practical matter quite difficult, even if it is allowed for Muggles who know about magic to be there without a wizard (which is never explained either way). This may be why we don’t typically see Muggle relatives alone in wizarding places - they’d be much more limited.
Most wizarding jobs require magic - Muggles could only do a few.
There’s nothing that states whether Muggles who already are allowed to know about the wizarding world through their relationship with a wizard can get a job in the magical world. However, even if they can, their choices would be severely limited since wizarding jobs typically require using magic. They couldn’t teach most subjects at Hogwarts (except for subjects like History of Magic and Muggle Studies which don’t seem to require magic to teach), they probably couldn’t do the majority of jobs at the Ministry, they can’t do anything that requires any use of magic. Their job options would, like Squibs’, be very limited. The two Squibs we know of, Argus Filch and Arabella Figg, are the Hogwarts caretaker and a breeder of Kneazles for wizard pets.
Muggles are not allowed to know about the magic world unless they are related closely to a witch or wizard. In the later case, I believe only parents, siblings or spouse would be allowed to visit the magical locations like Diagon Alley. However since these places contain so different objects, I highly doubt if any muggle can go there without a wizard.
Further, to travel to any such place, we need to use magic - which muggles cant do alone. Their fireplaces are not connected to the floo network and Tom wouldn't allow muggles to wander behind the bar to the entrance to Diagon Alley. They cant even apparate. Also we know when a student needs parchments or potion ingredients, they get it from Hogsmeade or get it delivered by owl from the shop. So certainly parents don't go there and buy stuff and then send by the house owl. Another point that even muggle parents would not visit the markets when not accompanying their children.
Having said so, I know an instance where a muggle was employed in the wizarding world - the muggle who was welcoming everyone during the Quidditch World Cup. Ofcourse his memory needed to be modified every few minutes so that he doesn't remember it.
To sum it up - you got to be a wizard or related to one to know about magic and magical places. The wizards might take your help in jobs or chores but you are not going to remember anything.