This is the example:
They will not accept your registration.
I have used akzeptieren.
Sie werden deine Anmeldung nicht akzeptieren.
Translator shows:
Nehmen sie Ihre Anmeldung nicht an.
As a native speaker what would you prefer as the right word in this registration context?
Your translation is fine, that one of the translator you use is completely off.
About the question, both akzeptieren and annehmen are synonymous in this context. But nicht akzeptieren is very formal speech and if used in an otherwise informal context, it means stern opposition.
Your translation is correct, the translator is plain wrong.
Both "annehmen" and "akzeptieren" mean the same thing here.
Please note that in common usage, "nicht akzeptieren" means I cannot accept it because it is too low/little/late, while "nicht annehmen" might also mean that it is too much to accept (for example concerning a gift).
