Learn French: Je ne pense pas que la proposition soit irréaliste. - I do not think that the proposal is unrealistic.

The phrase je ne pense pas que expresses doubt or subjectivity, which triggers the subjunctive in French. If the sentence were affirmative, it would express certainty in the speaker's mind and use the indicative: Je pense que la proposition est irréaliste.

Would a question like Do you think the proposal is unrealistic? also use the subjunctive?

Yes! Just like the negative form, asking a question with an opinion verb (like Pensez-vous que) introduces doubt about the outcome, so it usually triggers the subjunctive: Penses-tu que la proposition soit irréaliste ?

If I drop the ne in casual speech and just say Je pense pas que, does it still take the subjunctive?

Absolutely. In everyday spoken French, you will often hear people drop the ne and say Je pense pas que la proposition soit irréaliste. The negative meaning is still there because of the pas, so the subjunctive is still required.

I have seen irréel used for unreal. Why use irréaliste here?

Irréaliste specifically means unrealistic (impractical or not making sense in the real world), which fits perfectly with a proposal or a plan. Irréel means unreal in the sense of being imaginary, dreamlike, or physically impossible.