I've had a course that was held by ACM Fellow Tichy about parallel computing. He always wanted to translate everything into good German (he mentioned that most translations / texts in Computer Science are quite bad, as they use English terms as the writers didn't know that German ones existed). He used
multithreaded. He also spoke of
Threads. Although I think that
Threads is much more common than
Fäden, it is consistent with the other terms.
Hence, I would translate it like this:
Das Objekt ist nicht gegen Probleme der Nebenläufigkeit gesichert und darf nur in einfädigen Kontexten verwendet werden.
Alternatively, if you want a translation that uses the common words:
Das Objekt ist nicht threadsicher und darf nur in Single-Thread-Anwendungen verwendet werden.
Quite often, it is a good idea to take a look at the German wikipedia to find common translations:
I recommend to use the first version if you write an academic paper and the second version if you write some software documentation that programmers should read.