If Ravenloft is a demiplane, and a demiplane is an extradimensional space, can spells that create extradimensional spaces (like rope trick) be cast while in the realm?
Yes you can,
Spoilers for rules not plot ahead...
Page 24 in Curse of Strahd indicates the specifics but the properties of the Demiplane of Dread (Barovia/Ravenloft) indicates that such extradimensional constructs as created via Demiplane or Mordenkainen's Magnificent Mansion are subject to the same warping rules as found in Barovia. Thus you could indeed "camp" in a Rope Trick but can't then Planeshift out of that to escape Barovia whereas normally you could planeshift out of such things as Demiplane spells if you were on nearly any other plane.
No spell - not even wish -- allows one to escape from Strahd's domain. Astral Projection, teleport, plane shift, and similar spells cast for the purpose of leaving Barovia simply fail...
Then a bit later...
Magic that summons creatures or objects from other planes functions normally in Barovia, as does magic that involves an extradimensional space. Any spells cast within such an extradimensional space (such as that created by Mordenkainen's Magnificent Mansion ) are subject to the same restrictions as magic cast in Barovia. --Curse of Strahd P24 Alterations to Magic
The Mad Mage of Mount Baratok has Mordenkainen's magnificent mansion prepared and can successfully cast it.
The demiplane created by a spell like Mordenkainen's magnificent mansion (PHB. p. 261) still follows the same rules regarding planar travel, so while you can create and enter an extradimensional space, you can't then planeshift out of that extradimensional space to escape.
Is there any reason why you think it can't?
Rope Trick says:
At the upper end of the rope, an invisible entrance opens to an extradimensional space that lasts until the spell ends.
There is no reason if, having entered that extradimensional space, that I couldn't cast rope trick again and climb into a different extradimensional space.
Since the DMG says of Demiplanes
Demiplanes are extradimensional spaces ...
The same would apply.
Technically, all planes are "extradimensional spaces" the difference between Demi- and non Demi- one's is that the former are finite and the latter are infinite.