This is true with most every contract -- you commit to obligations, and agree to limit some of your freedoms in exchange for some benefits.
Of course such contracts are subject to, and must not violate, applicable local, state, or national laws, and any international conventions.
But that seems to not be the case here, as the legality was tested in the ECHR, and passed.
Generally, when disputes with athletes arrive in the courts, they are dismissed as the parties agreed to settle disputes in arbitration -- an acceptable form of justice recognized by the courts, for club disputes.
WADA works with governments several ways: through National Olympic committees, and National Anti-doping Organizations, and also by regional representation in WADA's board, and any number of committees and working groups.
Here for example is a footnote regarding how WADA worked with Europe, with athletes, with NADOs, with governments and with International Federations to update the Whereabouts rule:
I'm sure I quoted this statement from WADA before:
You keep citing the necessity to state that WADA is not acting above the law, but it's not clear that anyone else ever believed that, and it's clear that WADA is continuously working within the applicable laws and working with athletes on the best compromise to respect the athletes while making anti-doping as effective as they can.
I think Thomas does not have a huge reputational problem, except from the more extreme core zero-tolerance mentality "fans" of the sport.