Does English use "red thread" as expression for theme?
Solution 1:
The word thread itself has such a sense.
From Merriam-Webster, sense 3b:
A continuing element <a thread of melancholy marked all his writing>
I do not recall ever seeing 'red thread' used in English in such a sense.
In Chinese legend, a red thread of destiny is tied by the gods "around the ankles of those that are to meet one another in a certain situation or help each other in a certain way".
Solution 2:
In English, it’s a common thread.