No, it depends on the index in question.
But the point is that we have notable index funds which are marketed to customers as having the intention to own segments of the market according to certain rules, and they are changing those rules with relatively short notice and for reasons that seem suspicious to many customers.
I mean that your index doesn't even have to own a segment of the market. Just look at eg how the Dow Jones Industrial Average is constructed. When a company has a stock split, it changes its weight in that index. That has nothing to do with 'the market'. (Stock splits have approximately no influence on your weight in the S&P500.)
Or you could have an index that captures all the stocks whose ticker starts with X minus those that start with Y plus the current temperature in Frankfort, Kentucky, in Rankine degrees.
In the US, you would likely also have to pay capital gains taxes for such a trade. (I think.)
In Singapore, in contrast, swapping between funds like this would not have any tax implications.
There is a ton of research that almost every IPO on average goes down in the first 6 month. That's why they are not included by default.