You misunderstand me.  I agree, residence has nothing to do with this.  And I’m not suggesting that British citizenship will be withdrawn from anyone who currently has it.
Let me clear up a couple of things:
I’m not suggesting that British citizenship would be withdrawn from anyone who currently has it.  It could be, and it has been in the past, many times, but in this instance I am confident that it wouldn’t be.
1948 was 28 years after partition, but let that pass.  It’s not the case that anyone born in the Republic before 1948 has the right to full British citizenship; they have the right to British Subject status, which is a considerably lesser status and is not heritable.  The right arises because Ireland was, until 1949, in the Commonwealth, and anyone born in any Commonwealth country up to that time was considered to be a British subject.  (By a curious irony, British Subject status has been progressively dismantled.  People lose British subject status if they acquire the citizenship of any Commonwealth country, including British Citizenship.  The rump of British Subjects now remaining are nearly all people born in Ireland before 1949.)
British citizens living in Scotland at independence - which is most of the population of Scotland - would continue to be British citizens, I agree.  Deprivation of citizenship is legally feasible, but politically unthinkable.
But their children, born outside the UK after independence?  That’s not so clear.
The question is this:  If, after independence, a joint Scottish/British citizen has a child, and that child is born outside of rump-UK, will the child be a British citizen?
I suggest, first, the fact that the parent has Scottish as well as British citizenship will be irrelevant.  Nobody who would otherwise be entitled to British citizenship by virtue of birth to a British parent is going to be deprived of it because they are entitled to Scottish citizenship.  All that is relevant is the British citizen status of the parent.  So, is a child born outside the UK to a British citizen parent a British citizen?
The present law is that, if you’re born outside the UK to a parent who is a British citizen, whether you acquire citizenship by descent depends on the nature of your parent’s connection with the UK.  If your parent was born in the UK, then you are a British citizen.  But if your parent themselves acquired British citizenship by descent from your British citizen grandparent, then you’re not.  In other words, the outcome will depend on the place where your British citizen parent was born.
Current law just looks at the place where your parent was born and asks “is it in the UK?”  This is effectively the same as the questions “was it in the UK at the time of your parent’s birth?” or “was it in the UK at the time of your birth?” because, apart from what is now the Republic of Ireland, the answer will always be the same.  (And current law deals explicitly with the position of people born in Ireland.)
But that won’t be true after Scottish independence.  There’ll be a whole bunch of Scottish citizens, born in Scotland at a time when it was in the UK.  And if their children born in independent Scotland (or in a third country) apply for British citizenship, the outcome will depend on whether the “place of parent’s birth” test is applied (a) as at the date of the parent’s birth or (b) as at the date of the child’s birth (or (c) as at the date the child applies for British citizenship, but for simplicity let’s ignore that possibility).
If nothing else, the current law is going to have to be amended to make it clear whether the test looks to the state of affairs as at the date of the child’s birth or the date of the parent’s birth.
What position will the UK take?  Well, there’s a precedent.  This question already arises with respect to Ireland and there is an answer that applies to Ireland. Somebody born in (say) 1950 in the Republic of Ireland to parents who were born before 1922 in (what is now) the Republic Ireland is neither a British subject nor a British citizen, even though their parents are British Citizens by birth, by virtue of being born in (what was then) the United Kingdom.   Like any Irish citizen, such a person is not an alien in the UK, and has a right of entry and indeed a right to vote and to be elected to Parliament (which other EU nationals do not have), but they are not a British Citizen, and they cannot get a British passport.  (If born after 1949, they are not even a British Subject.)  Whereas if that person had one parent born in Great Britain or Northern Ireland, they would be a British Citizen.
In short, the established precedent is that, when territory has been ceded from the UK, the fact that a person has a parent who is a British citizen by virtue of birth in that territory before it was ceded from the UK does not qualify that person for British citizenship by descent.  You are only a British Citizen if the territory in question was still in the UK at the time of your own birth.
If they treat independent Scotland as they have treated independent Ireland, people born in Scotland and resident in Scotland at independence will continue to be British citizens, but their children, born after independence in Scotland or in a third country, will not be British citizens.
Of course, they need not follow the Irish precedent when it comes to Scotland; perhaps they won’t.  But they are at the very least going to have to think about it, and adopt a definite position one way or the other.  And I don’t think you can dismiss the possibility that they might follow the Irish precedent.  What reason would they have for treating Scotland differently?