In this modern world where gender equality is a given (in most countries), it is largely unacceptable to refer to the general “you” or “their” as the masculine “he” just as, in many cases, “spokesman” should be “spokesperson” unless referring to a specific person.
In many companies, gender equality policies are rife and it may be considered improper or offensive to submit a document referring to “the client”, for example, as “he must understand the product as best suits him”. Use gender neutral pronouns such as “they” and “them”.
But for the translation from Spanish, for example, where “su” refers to both males and females, this topic can be very confusing for native Spanish speakers. Just as the gender labeling of every object in the Spanish language is confusing for an English speaker!
To make it clearer, when translating “su” when it refers to a person in general, use “their”. When referring to an object or company use “its”. It still surprises me just how often such a translation pops up, for example, “The company sacked his employees” or even “their employees”. It is always “its employees”.
And if it seems more appropriate to use “he/she” instead of “they” or “his and her” instead of “their”, try mixing it up and putting “her and his” if you feel it suits.
If you are still confused about whether to use “his” or “their” or “chairman” or “chairperson”, ask the client and find out just what their gender policy is!