Technically, it would be correct to use 'he' everywhere, since in English that is what is considered the neutral gender. Second best is using He/She to satisfy the PC folks.
"Is considered". Considered by who exactly? How subtle of you to use the passive voice to plaster over the cracks in your argument :) There is no best, just norms surely.
That being said, there are ways to be gender neutral without dropping the clangers that this author does. Be gender neutral by all means but for the love of the children don't switch back and forth like an eager yo-yo.
