Also- I wonder what society's current warm fuzzy feelings about 'equality' might become next time the US must reinstitute the draft & folks start seeing their daughters being sent off to be wounded/killed in combat.
Of course, if there is a draft, women should be subject to it. And, anyone in the military can be wounded or killed, female or not. I don't personally value my daughter's life more than that of my son's.
One point that I also think is important is that women do get killed in combat now. Just because certain occupations haven't been open to them that doesn't mean that they can't be sent to combat zones and killed. Keeping women out of certain occupations does, in fact, keep some women from advancing who could advance more if those occupations were open to them.
As to whether standards should be the same for men and women, it depends on what the standard is supposed to measure.
For example on the fitness standards they differ between men and women - what is the purpose of the standards? Is it to determine whether someone meets minimum standards necessary to do certain tasks? Or is it to determine if someone has a healthy level of fitness?
If it is the latter then it would probably be reasonable to have different male and female standards. For example, take body fat as an example. Because of female anatomy what is a healthy body fat for women is higher than what is a healthy body fat for mean. This is biology.
A woman has less upper body strength than men as a whole - so a woman who can do X number of pushups would be a very healthy and fit woman while for a man that same number of pushups would not be indicative of being healthy and fit.
On the other hand, if the purpose of say a standard for pushups is to do a particular job and to do that job you need a certain amount of upper body strength and you can show you have it by being able to do X number of pushups then for that purpose the number of pushups required should be the same whether male or female.
In the past (not saying this is true now), physical standards were often set in some fields at a level that women couldn't meet when the job didn't actually require or need that level of physical fitness (to be absurd to make the point - requiring that you be able to do 150 pushups in order to get a job as a clerk. ). That is the standard was set with the design of keeping women out of it, rather than because the job required that standard.
TL; DR
If the standard is meant to show general healthy fitness and not for specific jobs then the standard should be based upon gender based norms as men and women do differ in what shows fitness for each (ex: body fat percentage)
If the standard is meant to show minimum qualifications to be able to competently do a job - the standard should be the same for men and women but it is important to be sure that the standard is really and truly based upon what is needed for the job.