As I have said, the pronouns they/them/their have become widely accepted in sentences with words such as anyone, someone, the person, nobody. More examples:
But they are less widely accepted in sentences such as the following:
Or in this one that I found in a book on learning vocabulary:
If you want to avoid problems like these, but you don't want to use the clumsy his or her / her or his, you will need to reform the sentence. You could do this by changing the singular noun into a plural one in order to match the plural pronoun. E.g.
Another approach is to alternate the male and female pronouns. This is what I have done in this series of articles. In one article I refer to the student or learner or child as a he, and in the next I will refer to them as a she.