It was considered distasteful.

There was a perception at the time that actors, musicians, and playwrights belonged to a lawless and bohemian class. They had a reputation for corrupting the innocence that (respectable) women were expected to maintain. If a woman appeared in a public performance in London in the late 1500s/early 1600s, it carried the connotation that her body was for sale.

A company of French performers attempted to break the taboo in 1629 by performing a show at Blackfriars that included actresses. They were booed, pelted with garbage, and driven from the stage. It wasn't until the Restoration (1660-1688) that women began to perform for the public.

This is Margaret Hughes. She may have been the first professional actress in England. She is said to have performed the role of Desdemona in Shakespeare's Othello on December 8, 1660. In 1662, King Charles issued a royal warrant declaring that all female roles should be played by female actresses.