As drspod said, no, Linux is not invulnerable. For Linux users using legacy BIOS boot or using UEFI but not secure boot, this vulnerability doesn’t make anything any more insecure than it was already. But any user, Linux or Windows, who is affected by this vulnerability (which is basically everyone who hasn’t revoked permissions to the Microsoft keys in question), if they’re using secure boot, no they’re not. (That is to say, they can no longer depend on any of the guarantees that secure boot provides until they close the vulnerability.)
As drspod said, no, Linux is not invulnerable. For Linux users using legacy BIOS boot or using UEFI but not secure boot, this vulnerability doesn’t make anything any more insecure than it was already. But any user, Linux or Windows, who is affected by this vulnerability (which is basically everyone who hasn’t revoked permissions to the Microsoft keys in question), if they’re using secure boot, no they’re not. (That is to say, they can no longer depend on any of the guarantees that secure boot provides until they close the vulnerability.)