Subjunctive in English. Is it used for politeness?

Solution 1:

Sometimes subjunctive moods are used instead of indicative tenses for politeness' sake, yes.

However, your example isn't a good example since it's actually a choice between either shifting to past-tense "were" in the ensuing subordinate clause to match tenses with past-tense "wondered" in the main clause or shifting from past-tense "wondered" in the main clause to present-tense "are" in the ensuing subordinate clause. You can tell it is actually a choice between indicative tenses and not a choice between an indicative tense and a subjunctive mood by simply shifting "wondered" to the present tense, like one would never say, "I wonder if you were free this evening." That sentence would only ever employ "are" to match tense with "wonder."

Nevertheless, it is true that subjunctive moods are used to express politeness sometimes. "If you happened to be free this evening, would you please come over for dinner?" for example, is politer than "If you happen to be free this evening, will you please come over for dinner?" since the subjunctive mood "happened" expresses true uncertainty, whereas the indicative tense "happen" tends to and traditionally does express a less-polite certainty suggestive of presumptiveness, in this case that tending toward less-polite, presumptive certainty being that the listener happens to be free this evening. Even if neither party — not the speaker or the listener — actually perceives such certainty from "happen" in that context, "happened" nevertheless remains politer because of tradition, tradition and customs being what politeness is predicated on.

By the way, another mood sometimes used for politeness' sake is the conditional mood (e.g., "would" instead of "will"). That's not just in connection with the examples in the paragraph above. Using the conditional mood to ask, for example, "Would you be free tonight?" is also politer than using the future indicative tense to ask, "Will you be free tonight?" Now, that doesn't mean that saying "will" is necessarily impolite, just that "would" is politer, the same being true for "happen" and "happened," respectively, in the paragraph above.