I think his homosexuality mainly gets brought up because of the manner of his death.
For instance, John Nash was apparently stripped of his security clearances due to being caught soliciting men in toilets, which wasn't even alluded to in the Hollywood version, but given that he wasn't then arrested and driven to suicide and furthermore is still alive and re-married (so we have to be 'sensitive' about him), this is not overly dwelt on by those who seek to tell his story.
For instance, John Nash was apparently stripped of his security clearances due to being caught soliciting men in toilets, which wasn't even alluded to in the Hollywood version, but given that he wasn't then arrested and driven to suicide and furthermore is still alive and re-married (so we have to be 'sensitive' about him), this is not overly dwelt on by those who seek to tell his story.