Why is this specifically relevant to Linux users?

Well,

• controlling end-to-end encrypted messages is only possible if either the keys/certificates are not secret (which is possible with TLS), or the software on the end-users device is not controlled any more by the user (but perhaps by law enforcement, or companies). This overturns the basis of any FLOSS software system where trust is based on transparency and user control.
• age verification will typically done by a form of attestation, a highly problematic concept. Again, this would require to run software on the users device which can’t be controlled by him or her, which is deceptively called “trusted computing”. (Technically, age verification could be done by other means, but this is not what these proposals aim for).
• in the world of public-key cryptography, which is what TLS , GnuPG, and most other modern systems are based in, encryption and digital signatures are nothing but two sides of the same coin: Who breaks encryption keys necessarily also breaks signature keys. This means it is not possible any more to sign software such as the Linux kernel, or Email clients, or browser packages. Or even banking apps or bootloaders for smart phones. Which means to give control away to the entities, groups or induviduals controlling these keys. Ironically, this will make computing lot less safe, and also undermine trust in communication networks, because communication where we can’t be sure that the communicated symbols are genuine is for humans as worthless as the numbers on fake money. (As a corollary, it is also bad for business: All business is based on some amount of trust. Would you do important business with somebody if the only communication channel you have happens to be a messanger which is a compulsory liar?)

To sum up, this is a massive transfer of control.