Like in most applications for naturalisation, the minister has a very broad discretion to decide who can and cannot qualify for citizenship.
It’s considered a gift and not a right, but similarly they have the same approach when it comes to what permissions that you have or what permissions you possess.
As a general rule Stamps 1, 1G, 3, 4 and 5 are considered reckonable, whereas Stamps 0, 2 and 2A are generally not considered reckonable. However with Stamp 0, our office is aware of a number of cases where people have been able to get naturalisation and that Stamp 0 has been considered reckonable but it very much is on a case-by-case basis and we would suggest if you’re in that category to seek professional advice before making that application.