Like many things in the Constitution, that only restricts the government. If they asked for this information, they'd need to get a warrant for it to be admissible in court.
Privacy right is not in the Constitution, it was created by the courts (IIRC there was a hilarious argument about penumbras of Constitution and stuff, but really, how credulous has one to be?). So I would think they may make it restricting anybody they like. And of course the Congress is the legislative body, which can legislate these restrictions, as it does with a myriad others. As long as the Constitution does not ban it, it'd be fine - and it's not likely that SCOTUS would consider right to privacy as contrary to the constitution, I think.