I was impressed to find out, that Transactions can have a pretty complex scripting logic (and they typically dont need to use that feature). One thing which catched my attention was the sample that you can require multiple signatures to be present. So if I sent a bitcoin transaction with a script which contains a "check if receiver has keya and keyb" I can determine if two addresses have the same owner - or more specifically are in the same wallet.

Is this correct, is this considered a privacy problem?

How (besides having multiple wallets) can I protect against that. Is there a way to not accept transactions with some scripts. Who is actually executing those scripts, and how are they asking me for the proof signatures? If my client is executing the script, can I lie about the interpretation result (since it is hashed in the block, but not necesarily possible to be repeated).

Greetings
Bernd