(1) I decided not to continue this diet program anymore.
(2) I decided to not continue this diet program anymore.
Is (2) absolutely wrong?
It isn't wrong, grammatically, but the preferred version would be (1).
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????Is (2) absolutely wrong?
In "traditional" grammar, we were taught never to "split" an infinitive. That is to never put an adverb between the particle "to" and the verb. But the split infinitive is used by many modern writers. So today's grammarians accept this construction. In your example, #1 is much better.