In Tonga people wear mats around their waist at any official situations, like going to church for example. Women sometimes wear smaller decorative things called kiye kiye, also plaited, but men always mats. Whenever I asked what was the reason for this, I was always told that this is to show respect.
I have never seen the use of mats this way either in Samoa or Fiji, which are quite close and of similar culture. I have seen similar mats being used in Vanuatu but only during traditional ceremonies. For example during a traditional part of a wedding, where similar mats were used like money, to pay for the bride (some pigs were apparently used for the same purpose). However, nobody used mats during the church part of the same wedding.
It is also interesting to note that in Tonga men seem to be more conservative in the way they dress than women. In most countries it is the other way around, women are more likely to put on traditional attire whereas men wear trousers and T-shirts. In Tonga women seem to wear western dresses while men come to church in a traditional skirt-like lava lava.