In English, when the gender is known, we use the pronouns ‘he’ or ‘him’ to refer to a man and ‘she’ or ‘her’ to refer to a woman.

• “If Mr. Brown calls while I’m out, tell him to call back later.”
• “If the lady calls while I’m out, tell her to call back later.”

When the gender of the person is not known or not relevant, and because English has no specific non-gender pronoun to refer to a person in the singular, the pronoun ‘he’ or ‘him’ was traditionally used as a generic pronoun.

• “If anyone calls while I’m out, tell him to call back later.”
  

Nowadays, because ‘he’ and 'him' are no longer accepted as a generic pronouns to refer to a person of either sex, it has become conventional to use ‘they’ or ‘them’.
For the same reason the gender-free pronoun ‘their’ is used to replace his/her.

• “Someone said that they saw a man running away with the suitcase.”
• “Each person was asked what they wanted for lunch.”
• “If anyone calls while I’m out, tell them to call back later.”
• “I’m looking for the owner of this phone to give it back to them.”
• "The person who called didn't leave their name."
• “Oh, someone has dropped their key. I’ll leave it at the reception.”
• "Any parent would be worried about their child given the circumstances."

Those who are unhappy with this could avoid the problem by rewording their text.
For example :

• Can you tell someone’s character from what they wear?
• → What can you tell about people from what they wear/from their clothes?

Another possibility would be to use ‘he or she’, ‘him or her’, 'his or her' or 'himself or herself’, but this can become awkward with repeated usage.
For example :

• If a patient has a problem, he or she should speak to his or her doctor.

The use of a plural pronoun to refer back to a singular subject is not something new. In fact it dates back to the 16th century and is now widely accepted both in spoken and written English. Here is an example of 19th century use :

“It’s enough to drive anyone out of their senses.”
- GB Shaw, Plays Pleasant and Unpleasant (1898)”

However it should be noted that some traditional grammarians still consider this usage to be unacceptable in formal writing. So when writing in a very formal context it might be advisable to reword the text in order to avoid this, but in any other register it is perfectly acceptable.