I'm not too familiar with Koine Greek (except getting a grade C for introductory Koine Greek in Bible school). As well as, since the septuagint is not dependable translation, and should not be used authoritatively. I can only comment better on the Hebrew.
Deut 32:21 (I placed a hyphen to separate the pronouns)
The word-literal translation (presuming a non-existent causative):
They jealousified me
(without presuming any causative):
They are jealous of me
The translators have again made wide excursions into "untreaded" territory, because [בלא] has been used as without, not within, not in, which are all similar concepts. The word literally means "not in" or "not within".
To translate the phrase as
They jealousified me with which is not G'd
is an adventurous trip to add in words and concepts not found in the original Hebrew.
(I had to coin the word "jealousify" to accurately portray the causative.)
OTOH, this verse indicates atheism or agnosticism in ancient Israel. Regardless of the instruction of "you shall not bow down to other gods", reading this verse at face value, in simplicity,
These atheists/agnostics are jealous of me.
בגוי נבל אכעיסם
The word-literal translation (this time there actually is a causative):
And I will jealousify-them
without a people
in a withered/decadent nation I will anger them
Therefore, without any regard to massaging the Hebrew passage to turn this into a scaffolding support for pre-existing doctrines,
Without a people, I will cause them to be jealous. I will cause them be jealous by not having a people. I will anger them with a decadent nation.
We must read the Hebrew grammatically as-is, rather than manipulating them to fit into pre-existing ideologies.