Completely agree with museumum's points.
Really importantly - every single island is unique. Even the north and south of the same island can feel worlds apart. Our language and culture is really important, and thankfully is becoming more widely recognised and protected.
One of the main things which this thread demonstrates is that you'll get so many people (mainlanders, visitors, people newly relocated to islands) telling you with complete confidence what a place is like, and they are completely off the mark. I can see utterly false statements in this thread like that about my own island.
Do your research. Visit multiple times, at different times of year.
For the island I'm from (but I can't speak for others) I wouldn't expect you to be greeted with open arms by everyone. Housing availability and affordability is a nightmare due to holiday homes and second homes.
It is an incredible place to bring up children, their primary school education (at the right school) can be fabulous. Outdoor learning is one day a week, every week, year round where mine went. But mine were born here, island life is all they know. It can be very different with kids moving from elsewhere.
Fuel, food and cost of living is more expensive, but you weigh it against the benefits you get. The weather is wild, the winters are dark, the summers are manic. The slower way of life is a myth. Islanders work hard to be able to afford to exist here. Yes some people have remote jobs, but others work multiple manual labour/service jobs to get by.
If you last two winters, you'll probably make it. But locals can, respectfully, usually tell who won't.