I'd say I'm broadly against it. It isn't that I think they're incapable of taking a bullet or delivering fire or following orders or any of that nonsense - no one is particularly well suited to being shot at regardless of gender. The problem is simply that it doesn't seem particularly worth the effort.
First, from personal experience, it was rare that I encountered a female in the US Army who could actually physically perform the job of an infantryman (for example). I'm not particularly convinced this is due to that classical "feminine weakness" so much as it seems to be a cultural thing - the female soldiers simply didn't want to do the sort of workout that would give them the condition necessary to perform the tasks. That some otherwise normal women were perfectly capable of doing the ruck march in the right amount of time or passing other physical standards set for males seems to imply that this shortcoming was a personal failing rather than one that broadly affects all women.
The second is a health concern - simply put, women are more prone to very specific types of injury. Hip injuries for example are an incredibly common malady in Basic Training. Beyond that there are additional considerations of hygiene and health associated with the menstrual cycle along with the associated changes in hormonal chemistry over the course of the cycle. Finally, there is that eternal bugaboo, pregnancy, which more or less forces a soldier in a combat role to do something else for months if not years afterwards. Again, not to assert that this would somehow make them incapable of serving; it simply presents a complication in logistics across the board that are not present with male soldiers.
The thing is, I am entirely certain there are women who could do any job in a modern military. The problem is, because of the issues with simply finding a female that meets the physical standards and then dealing with the higher risk of common injury that would prevent them doing the job, it simply doesn't make a lot of sense to try. To put it simply, if a significant number of females are, for one reason or another, incapable of performing the job, then having lots of them try out (at an egregious cost to the taxpayer - training of a soldier can cost several hundred thousand dollars for certain jobs) and then fail only to be reclassified and sent to try again seems silly.
I suppose there is a simple answer to that problem in the form of simply having a series of tests designed to weed out those obviously incapable of making the cut. Of course, since such tests do not exist for males (since the average 18 year old male has demonstrably proven themselves capable of meeting the standards) I would expect this would elicit an outcry of unfairness.
Of course, there are other issues that are far harder to define that I don't particularly believe. There are wide ranging theories (almost certainly based on nothing more than bias) that including women in combat roles intentionally is foolish. For example, western civilization is more or less hard wired to be appalled at the death of "women and children" - the adult male by contrast is seen as expendable and only worth mention by exclusion. While no society is comfortable with sending people to die, some would argue we are far less comfortable sending women to die for a cause. Then there are various theories relating to gender politics that would assert the inclusion of sex (the natural result when you stick a bunch of twenty-somethings in close quarters for long periods) would be detrimental to the chain of command and disrupt unit cohesion. You might recognize that last one as one of the many arguments used against letting openly gay soldiers into the military. All of these have at least some element of truth in them but, given that I've never seen a real academic study on the subject, it's hard to determine just how big a concern such things are. For example, if we are less comfortable sending women to die, in the event of a hard fought war with high casualties, does that affect the total number of casualties we'd be willing to accept before seeking other options? And while sex within a group has a profound impact on group dynamics, is it necessarily a negative one from a military perspective?
When you get right down to it, the question really comes down to a wholly pragmatic quandary: would the military be improved, on the whole, by letting women serve in combat rolls? I don't see any reason to believe a military facing anything short of an existential threat would see an improvement and even then it's only on the basis that such a crisis would require as many soldiers as possible at whatever the necessary cost. Such threats are rare in the modern world - at least threats that can be fought with rifle and bayonet.