I know it's been awhile since there's been a post but figured I'd share in case it might help someone down the road.
It's kinda funny, but I think family disapproval has more to do with your parents/relatives feeling abandoned/not being able to "access" you and/or having "empty nest" syndrome.
Both my parents were prior enlisted Air Force (plus my Oma was former Army nurse back in Korea/Vietnam, grandfather served in WWII), 100% supported my brother's interest in the military, but didn't approve mine. When I told my parents I was enlisting, my mom was absolutely livid and my dad was just, indifferent, only asked that I not immediately get knocked up and married in my first year (ironically, two things they now are concerned I'll never do lol). For them, I think it was mostly empty nest syndrome kicking in and the fact that my brother will always come back home if asked and I was always adamant about leaving. When I was traveling to my first duty station, I stopped by to visit them (out of courtesy) and my mom started treating me like I was in high school again, demanding I take every holiday leave to visit them, asking for access to my banking accounts, etc... Basically told her that I had no financial ties to her, no legal obligations to her, and that I never would have to visit or see them again if I didn't want to because I was a grown adult with a steady income.
Believe it or not, our relationship has dramatically improved since then. It's like picklesuit said, if they don't pay your bills, their opinion doesn't matter. Set boundaries and succeed in your job. Who knows, time may change their minds.
Thanks for coming to my TED Talk.