There is an astonishing number of people who believe in conspiracy theories now. On the FB page of my local newspaper,, for example, practically every other post cites a conspiracy. I'm sure there wouldn't be so many in normal times. During times of crisis, people look for someone to blame. In the past, it has been witches, Jews and Catholics.... Now it's Bill Gates, Big Pharma, Hillary Clinton and her circle of blood drinking Satanic paedophiles... Predictably, there's a tinge of antisemitism in these theories. George Soros/the Rothchilds are often referenced, usually as shadowy figures pulling the strings.
What these people need is a good dose of Occam's Razor, a philosophical principle which says that, if there's more than one explanation for something, the one that requires the least assumptions is the most likely to be true. In other words, the simplest answer is the most likely to be right. However, people deep in conspiracy theories are so busy disappearing down the rabbit hole that it becomes difficult to stop and say to yourself: is this true or is it, in fact, a load of rubbish?
I don't know whether this amounts to a mental illness. No disrespect to the religious amongst us, but most (all?) religions require believers to accept as fact all sorts of incredible stories. We don't call these people mentally ill unless the stories take over their lives.
It sounds as if this may be happening with your sister, given her personality changes. People have mentioned dementia, which is a possibility, but it could be the effect of immersing herself in stories which thrive on fear and a sense of powerlessness. Fear tips over into paranoia. It is extremely difficult to get anyone to seek help, particularly for mental health issues, if they don't recognise that they have a problem. You're also at a disadvantage if you live far away. All you can do, I think, is to continue to support your brother-in-law and try to keep your conversations with your sister as normal as possible.