Traditionally no man older than 19 would be cast as a woman because his voice would be too low.
Choosing to stick with what was known as original casting could be well-meaning but in effect it just further blocked women from participating in Shakespeare, Reid said.
"Only 12 per cent of Shakespeare's entire roles are female and that means already women are under-represented in what is the most dominating playwright in Western history so why would you go even further and cast all men?
"It is sexist. It's invisible sexism."
Auckland actor Rosie Cann, 22, said she believed the tradition of men playing female roles was outdated and should fall by the wayside.
"The idea of the tradition isn't appealing to me as a modern-day actor because it is based on something we're trying to culturally expunge.
"Local actors need work. It's a rare, high-paying opportunity. A really important opportunity. Basically local female-identifying actors missed out."
Cann told the Herald it was part of a wider problem female actors faced. Roles for women were often less interesting, less developed and there were fewer major roles to go for.
Cann has previously read scripts only to realise she was just a "tag-along" character.
"It's hard to audition intelligently for a role that is underdeveloped. It's hard to go for a character that has no meat ... Being someone's girlfriend is not inspiring.
"Once I realised what was going on, you can't unsee it."
She said last year some women reversed the convention and had an all-female cast put on a Shakespeare play. They called themselves the Lord Lackbeards and their lead actor was six months pregnant.
"Which was so amazing. So much more interesting to watch than straight white dudes."
Pop-up Globe director Tobias Grant said in the age of Shakespeare and the 44 years after his death until 1660 it was illegal for women to perform on the public stage in England.
Consequently the male and females parts in Shakespeare's plays were written to be performed by men.
"There are many references to this fact within Shakespeare's plays. For example the female character Rosalind in As You Like It says to the audience at the end of the play, 'If I were a woman I would kiss as many of you as had beards that pleased me.'
"We believe that because Shakespeare originally wrote his plays for an all-male company, part of our artistic output should incorporate all-male productions performed in historically accurate costume. Accordingly one of the companies in our 2017 acting ensemble is an all-male company."
The second company is mixed with male and female actors who work with directors who are free to tell the story as they choose.
Grant said of the 84 people who work with the Pop-up Globe organisation 40 were women including the general manager and head of sales and marketing.