By that measure, having women priests/ministers (or just letting a woman conduct a reading, as even the Catholic Church does) is also a no-no:

"Let your women keep silence in the churches: for it is not permitted unto them to speak" -- 1 Corinthians 14:34.

And clerical celibacy is also out:

"A bishop then must be blameless, the husband of one wife" -- 1 Timothy 3:2.