Is ‘they’ acceptable as a singular pronoun?

Every time I use “they” as a singular pronoun in one of my articles, someone posts a comment, or emails me, scolding me for my grammatical error. My response? I (politely) tell them to get over it.

Granted, multiple grammatical strategies are available for people to identify someone with a personal pronoun, each of which can be used exclusively or in combination with one or more of the others:

Use the male gender: “Each person is entitled to his opinion.”

Use the female gender when all possible referents are women: “Each nun is entitled to her opinion.”

Use both male and female genders: “Each person is entitled to his or her (or his/her) opinion.”

Alternate gender references in repeated usage: “Each person is entitled to his opinion. However, she should also be receptive to those of others.” (This strategy is best employed with distinct anecdotes in separate passages; it’s awkward in proximity as shown in this example.)

Use an indefinite article in place of a pronoun: “Each person is entitled to an opinion.”