Church documents express a preference for men as EMHCs, which I agree with.
From the 2002 General Instruction of the Roman Missal (GIRM) approved for the USA, which can be accessed from
romanrite.com/girm.html :
“100.
In the absence of an instituted acolyte, lay ministers may be deputed to serve at the altar and assist the priest and the deacon; they may carry the cross, the candles, the thurible, the bread, the wine, and the water, and they may also be deputed to distribute Holy Communion as extraordinary ministers.”
Only men can become instituted acolytes (Code of Canon Law, canon 230), and they are to be used before other EMHCs.
The liturgical books encourage the use of instituted acolytes, particularly the 1984 Ceremonial of Bishops, n. 28 “But in celebrations presided over by the bishop it is fitting that all such ministerial functions be carried out by formally instituted acolytes …”.
Any man has the possibility of being instituted as an acolyte, no woman has. So, if all else is equal, the priest should choose men to be EMHCs, in the absence of instituted acolytes.
I would apply the same reasoning to the choice of readers. If there is no instituted lector, men should be the preferred choice to read. This provides encouragement for them to become instituted lectors.
The habitual use of men in these functions would also reduce the pressure on bishops in deciding to instituted men as lectors and acolytes. Many bishops seem reluctant to institute men to these ministries, because then women who do these functions will be denied their role. If more people encouraged women not to take up these roles, priests would stop choosing them and bishops may be more prepared to instituted lectors and acolytes.