Is it acceptable to use THEY instead of HE or SHE?
The English language unfortunately lacks a simple singular pronoun which does not specify gender. Various people have suggested new words to fill this gap, but none of them has caught on or (frankly) is ever likely to. It is not practical to try to change such a basic element of the language by sheer will.
However, children and adults alike naturally find the obvious solution to this conundrum. Rather than using the formal and awkward formula he or she, they simply use they especially after words such as anyone and no one which are strictly singular but often imply a reference to more than one person.
This is not a new problem or a new solution. 'A person can't help their birth', wrote Thackeray in Vanity Fair (1848) and even Shakespeare produced the line 'Every one to rest themselves betake' (in Lucrece) which pedants would reject as logically ungrammatical.
If you do not find this usage acceptable, there are alternatives. You could resort to the awkward he or she formula or to the practice of writing he when you mean he or she (which many people find objectionable) or to recasting all your sentences to avoid the problem!