Sanitarium is not a charity, it's your average, normal company (actually two companies).

Seventh-day Adventist Church is a charity. The Charities Act 2005 lists "advancement of education or religion" as a charitable purpose, so the Charities Commission are unlikely to have any say in whether they are a charity unless they can prove the church is a sham.

The reason Sanitarium pays no tax, is because any donation a company makes to a charity is (rightfully) tax deductible. Sanitarium need only donate the amount of money they made as a profit and now they have no tax to pay. Any company could do this, if ANZ donated all their profits to the Cancer Society they would pay no tax. But there would also be nothing for shareholders, so they don't do this.

Because SDA are the shareholders, they pay the profits as a donation instead of a dividend to avoid tax.

The only problem I see in any of that is that churches qualify as charities simply by advancing religion. If you removed that requirement, most small churches are likely to still qualify as charities under either reducing poverty, if they do that, or under the more general benefit to the community so long as they do something that is actually beneficial. Many small churches do actual charitable things for their communities, but I think large ones would have a harder time proving their community value.

I'm generally not against a charity being able to invest spare cash to better fund future years, but my opinions on things are pretty easily swayed 😆