Culturally, women could be trained to be just as brutal and violence-prone as men. Most cultures have never supported that notion, however.
A woman warrior or combatant is not unrealistic physically. Currently, it seems improbable because of cultural institutions and mindsets ingrained throughout generations. Women are peaceful blah blah.
Women naturally have less strength than males, yes. They have a lower "starting point" in strength and a lower "max" as well. However, strength does not always overcome skill. As stated, if women were incapable of using a bow and arrow, a crossbow would be a fine alternative. Women could become expert sharpshooters with terrific accuracy. Male and female genetics won't make men the naturally better shooters, just simple practice and natural skill will.
In addition, though many fantasy genres play up the concept of "female agility," aka rogue roles, I don't think that we have to fallback on that role to be realistic. A woman warrior is quite realistic. Sword combat isn't all about putting 100% of your strength behind a blow, it has skill involved as well. Yes, strength plays a determining factor in winning out blow for blow, but technique can overcome that. There are many men that are physically weaker (even by extreme amounts) than other men, but still beat them in martial arts or other combat situations. Physically weak women are just as capable as physically weak men.
Break down those cultural norms, dawgz. However, if you're going for cultural realism, sure, protest the use of female warriors.