If you make sure you "pre-anonymise" your data so that even you have no clue what you're uploading then there will be no way these agencies can find out!
Of course a downside could be value of said random data, but hey; at least its anonymous...
Ok, a little more seriously: the real solution should be obvious enough; if you require privacy then why share your information in the first place?
Both Google (YouTube) as well as Microsoft (Microsoft ID) are both currently doing their best to persuade me to use my real name and information. Google is a bit more intrusive than MS on this, but even so; they're both persistent.
And I keep telling them "forget it". Right up to a point where I might go "Screw it" (YouTube) but we're not there yet. How many people do allow themselves to be suckered in only to wonder a few months later how its possible that their name seems to end up all over the place ?
Privacy starts with yourself.