Is it forbidden to use a language learning program that requires the translation or speaking of sentences containing prohibited phrases such as "I love wine," or sentences that necessitate expressing non-Islamic religious beliefs such as "I am Jewish," knowing that these sentences cannot be skipped?

What you mentioned does not prohibit the use of these programs. Indeed, repeating sentences to learn a language does not incur sin. Merely repeating or quoting speech for learning purposes does not necessitate believing its meaning, affirming it, or being pleased with it. Ibn Muflih said: "One who repeats disbelief that he heard does not become an unbeliever, nor does he believe in it, and perhaps this is a consensus."