A democracy is about people whose lives will be significantly affected by a decision having a right to take part in the decision-making.
Why this logic was applied to resident Commonwealth and Irish citizens differently from residents from EU?
Regarding Commonwealth citizens - I'm not sure of the logic, but it has something to do with Britain occupying them... At any rate, these are legal loopholes and not the standard state of affairs.
I presume it's related to their historic status as British Subjects (which some of them will still hold, though it's been impossible to gain status as such since the 1980s), which would have granted them the right to vote in Westminster elections and referendums.