Gays are not just in the military. They are everywhere, and deserve just as much freedom as anyone else. Why should someone who is attracted to the same gender be subjected to punishment. Are they hurting anyone by being gay? No. They should have rights because they are human. They are exactly the same as everyone else. They just want to live their life with someone of the same gender.
Why do you deserve civil rights? What have you done for society. Thousands of gay people have served in our military, worked jobs, worked for the government, helped feed the poor, adopted children to loving homes, donated to charity, done charity work. They are the exact same as everyone else they just love the same gender. You seem to think they are some new world of people that just started existing and are demading to be elevated above the rest. When they just want the same rights as everyone else and who are your or anyone else to decide that they shouldn't be allowed to have rights? Just because they are different they deserve the short end of the stick? How would you feel if you were born with a tail and your rights were taken from you because of something you were born with? "You have a tail and all people with tails shouldn't be allowed to have civil rights" I imagine you wouldn't be very happy.
Are you aware what a "Civil right" is? A civil right by definition is "A civil right is an enforceable right or privilege, which if interfered with by another gives rise to an action for injury. Examples of civil rights are freedom of speech, press, and assembly; the right to vote; freedom from involuntary servitude; and the right to equality in public places. Discrimination occurs when the civil rights of an individual are denied or interfered with because of their membership in a particular group or class. Various jurisdictions have enacted statutes to prevent discrimination based on a person's race, sex, religion, age, previous condition of servitude, physical limitation, national origin, and in some instances sexual orientation"  So, yes it would be. You have the right to be gay. You are allowed I suppose under the freedom of expression. There is nothing that says otherwise. Why shouldn't it be a civil right besides a biased opinion?
Yes being gay is a civil right. You have the right to be gay as it is a freedom of expression. You may express your love for whom ever you like. There is nothing stated otherwise and you have provided no proof that it isn't a civil right. Other than saying "no its not because I say it isn't"