Before someone asks: Yes, I was a soldier. US Army 11B.
I answered No, however, this is not really a question of "should," and the answer is not as simple as "Yes" or "No."
Obviously, if you ask "should" a woman be allowed to serve in a combat arms (boots on the ground) role, the answer is "of course, so long as she can meet the exact same minimum physical standards as any male soldier." Yes, there are women out there who can do that, though it's not really as normal as some people like to make it out to be. Carrying a 200lb injured man, with his 20lbs of attached equipment (not talking about his weapon and dropped ruck, which is another 45-80lbs) out of direct fire is not an easy thing on its own, much less dragging him to where he might need to go to get actual help. A lot of men can't do that, either.
But, the real questions that have to be asked is "who are we fighting" and "what are the rules of engagement?"
If this was X-Com, or Starship Troopers, where the enemy is some monstrous alien being or some form of animal with no physical relationship (and, thus, no sexual relationship) to humans, then the answer, for me, swings closer to Yes. In that situation a woman cannot be exploited by an enemy to the detriment of her comrades any more than a man can be. Equal risk.
If this some number of centuries ago, where it was normal rules of warfare to rape and pillage the countryside when victorious, then the answer is very much "Yes." If a woman is likely to be exploited/raped/murdered anyway, then let her fight. Same risk in either situation.
However, under modern rules of engagement and most (probably faulty, but I don't make them) expectations, civilians are either killed as collateral damage or avoided, but not purposefully raped and murdered. Obviously, there are exceptions, and they may be more the rule than the expected ROE, but the ROE is made under the pretense that the various Conventions apply. In this situation, I vote No. It has nothing to do with a woman's ability to fight, but rather with the ability of her to be exploited to the detriment of others. The threat or actual act of sexual abuse/torture against a female companion is a very powerful coercion technique. It will break people, I guarantee. Limiting this threat by limiting women to combat support roles is not necessarily a bad thing. It isn't evil or negative comment on female ability, in and of itself (though I'm sure it can be used to cover that up quite often). <~~~ This is my primary concern.
Also, there is the very good point that men are men and have natural tendencies to behave sorta like... well... men. They will form protective bonds with people around them, male or female, but their protective behavior towards women will tend to be more pronounced. This could potentially cause men to do some really stupid things in combat to protect a female comrade. However, this is one of those things I think men should be able to learn to get over. <~~~ A concern, but one that I think needs to be dealt with and dropped, rather than hidden behind.
That said, I am generally in support of women in combat roles where they are not part of a ground squad. While some of the same arguments above about using the threat of exploitation of a woman vs. male counterparts still applies, it is more mitigated in a situation where they are not part of an infantry type unit. Female combat pilots in both Air Force and Army aviation, I think, are perfectly great. Women serving on warships is fine with me (the pregnancy concern is very real, but I think there are ways to deal with it, rather than just hiding from it... people may not like the ways of dealing with, but equal rights means equal responsibility).
Anyway, I'd love to say yes. There are a lot of situations that I'd say "Yes" in, because I think women deserve the right to fight for themselves or others. However, in modern ROE warfare where the enemy is always another potentially disgusting human being, I still think the modern day infantry unit is safer being all male.