No, they can’t.  Think about it; if what you say were true, then British citizenship could descend generation after generation to ever-larger numbers in families that had left the UK many generations ago and never returned.  But, as we know, it can’t.
In general, if you’re born outside the UK, being the child of a UK citizen is not enough to give you UK citizenship yourself unless your parent is a British citizen “otherwise than by descent”.  So if your parent was born in the UK, or immigrated to the UK and was naturalised there, you’re good.  But if your parent was a British citizen because their parent was born in the UK - i.e. your parent is a UK citizen by descent - then you’re not so good.  (In certain cases your parent - the one who is a British citizen by descent - may be able to register you as a British citizen, provided they do so before you turn 18, and provided they themselves have lived for some time in the UK or in a British Overseas Territory.  Or there are a couple of other conditions they may be able to satisfy.  The point is that as British citizens by descent there is no general right for them to register their children as British citizens; they need a further connection with the UK. )
[quote=“Pjen, post:495, topic:685820”]
What you are suggesting is that someone born in Scotland living in California would not be affected by the decision of part of the country purely dependent on the whims of the people left in Scotland, but someone born in Scotland living in Scotland would not.
[quote=“Pjen, post:495, topic:685820”]
No, I’m not saying that.  The rule will have nothing to do with your parent’s residence.  As I have said before, residence does not enter into it at all.  It will have to do with your parent’s place of birth.
Assume A is born in Edinburgh in 1990.  In 2012 A has a child, B1, born in Edinburgh.  In 2014 A has a second child, B2, born in Paris.  In 2015 Scotland becomes independent; A acquires Scottish citizenship but does not lose UK citizenship.  In 2020 A has a third child, B3, born in Edinburgh.  In 2022 A has a fourth child, B4, born in Paris.  It will work like this:
A is a British citizen by virtue of birth in the UK, and therefore under current law is a “British citizen otherwise than by descent”.
B1 is born in the UK; by virtue of that, B1 is a British citizen.  And, since B1 is a British citizen “otherwise than by descent”, any children that B1 may have, if born outside the UK, will also be British citizens (but by descent, so the automatic transmission of citizenship will stop with them).
B2 is born outside the UK, but has a parent who is a British citizen otherwise than by descent; B2 is a British citizen by descent.  Any children B2 may have, if born outside the UK, will not be British citizens.  (However if B2 lives for a period in the UK or a British overseas territory, he should be able to register his children as citizens before they turn 18.)
B3 is born outside the UK, but has a parent who is a British citizen otherwise than by descent.  If the law is unchanged, B3 will be a British citizen by descent, and cannot transmit British citizenship to any children they may have outside the UK.  (But, if the conditions are satisfied, the possibility of registration arises.)
B4 is born outside the UK, but has a parent who is a British citizen otherwise than by descent.  If the law is unchanged, B3 will be a British citizen by descent, and cannot transmit British citizenship to any children they may have outside the UK.  (But, if the conditions are satisfied, the possibility of registration arises.)
The first point to note here is that the situation of B3 and B4 is identical.  It makes no difference that one was born in Scotland and one was born in a third country.  All that matters is that both are borne outside the UK.
If the law changes to assimilate the treatment of independent Scotland to that of independent Ireland, it will change for B3 and B4 alike.  Again, it will make no difference that B3 is born in Scotland and B4 is born in Ireland.
Why should the law change?  Well, because they did change it with respect to Ireland, and the change makes a certain amount of sense.  The question of whether British citizens passes down the generations depends on the nature and degree of the British citizen parent’s connection with the UK.  If your parent was born in (say) Galway, and Galway is not in the UK, the fact that it once was, and the fact that it was when your parent was born, is not seen as a close enough connection with the UK to justify conferring UK citizenship on you.  On your parent, yes, but not on you.  By the time you are born, your connection through your parent is to a place which is not in the UK.  So, under current law, a person born in in Galway before 1922 is not considered to be a “British citizen otherwise than by descent”, and their children are not British citizens.
As I’ve said already, it’s not a given that they will assimilate the treatment of independent Scotland in this regard to that of independent Ireland.  But it’s obviously something that they might do.