As founder and ongoing volunteer with SDN, I assure you that your .mil email is not being used for anything other than verification. It is not saved on our servers or linked to your account (unless you've chosen to make it your member email too) -- so even if the military tried to subpoena your information there's no record of it on our servers after the verification is complete.
FWIW, in the past 12 years, we've only been successfully subpoena'ed once for member information and that was for a clear-cut copyright violation. So as long as you're not sharing government secrets or posting illegally copied materials, you should be OK.
I'm Army myself - but don't fly the badge because of my other volunteer duties that I have at SDN. However, if I wasn't doing my volunteer work with SDN, I'd definitely have the badge -- it's not necessary, but it does make it easy for other members to identify who has been verified as being in the military. Plus getting all the Google ads removed from the site makes the site load faster, which is sweet.