There is a barely perceptible illogicality in this formulation, and this is because of the defining (also called "specifying") nature of the part "which was back then so new and fascinating". In other words, you shouldn't write down such sentences because they amount to nonsense.
The basic statement is the assertion of a sufficient curiosity in order to do sth. This sth has to be defined next. It is "to care about X".
- I was sufficiently curious | to care about X.
"X" can be "something" and that makes for an acceptable statement, that can have more than one purpose. To simplify "new and fascinating", let's restrict our attention to "fascinating", which has truly the advantage of being gradable. So, we can say this, which specifies further "things" and makes the sentence a more edifying utterance.
(diversion) As such, that is, as a defining, specifying or (still equivalently) restrictive addition (no comma is used before "which"), the sentence is syntactically well constructed; however, were the clause to be non restrictive and merely descriptive (no comma), the result, if still grammatical, is, in the absence of context an ambiguity.
- I was sufficiently curious | to care about | something, which is fascinating.
The second version can be "specialized" to the past and we obtain this.
- I was sufficiently curious | to care about | something which was fascinating.
The idea of fascination is absolute in "1"; if we relativize this idea by the addition of the time adverbial "then", both versions "1" can be specialized to the past and are equivalent.
In this final formulation you classify the thing among those that were fascinating but which are not necessarily so any more; in so doing you are saying that the curiosity was sufficient for things that were bound to lose (more or less) their status of fascinating thing; but there does not exist the slightest criterion enabling one to connect the sufficiency to the change of category. I believe that that is what makes this sentence an undesirable construction.
This rather imperceptible effect of inappropriateness would not be felt in formulations such as the following.
I was sufficiently curious to care about something, a thing then fascinating.
I was sufficiently curious to care about something, and that thing was fascinating then.