Utter nonsense I'm afraid. Sweden is "required" to join the Euro and has no opt out but no one can force them to join ERM (a prerequisite to joining the Euro) so they have happily maintained the Krone for nearly 20 years without anyone forcing them to join the Euro.
This was an oversight in its specific treaty of Accession to the Union.
That mistake has not been repeated since and will never be repeated again.
All later-joining members are bound to join ERM-II and thus the Euro.
Equally Cyprus is "required" to join Schengen but chooses not to as it would be inconvenient in relation to border crossings with Northern Cyprus. (an island which has two entities not in Schengen so they choose to remain outside, does that ring any bells?)
The Cypriot situation is rather unlike any reasonable situation that could arise in the United Kingdom.
The Cypriot exception is a result of the whole truce-in-an-effective-civil war thing, complete with a UN peacekeeping force.
Cyprus claims the entire island as its territory and as such joining Schengen would cause a diplomatic incident with the Turks who are the only country to recognise the other state on the island.
And that is assuming that Scotland cannot negotiate a new opt out.
The Scottish Government has absolutely no leverage to gain an opt out.
The French and Spanish governments use the argument that any seperatist state would have to start at square one against their own seccessionists (especially the Basques and Catalans).
Giving Scotland any ground at all would undermine that argument.
I suspect the other countries' main concerns would be removing the financial opt outs. No one is going to force Scotland to join the Euro or Schengen out of spite and even if they were mad enough to do so there are countries who have informal opt outs at the moment so we can see how Scotland could stay out unofficially.
Those informal opt outs are all the result of specific circumstances that the EU Commission is wise to and will not allow to occur again.
Unless you suggest that there will have to be a UN police truce-line in the Scottish Borders, complete with neither state recognising the other?
As I say independence probably won't happen and I don't personally support it but these sort of nonsensical Westminster scare tactic debating points add nothing to the real discussion.
The problem is that the Scottish Nationalists just rant and rant and expect that all these problems will magically solve themselves in ways that they want
simply because they want them to.