The Microsoft press release is very light on details:
The fact that ARM and Intel are involved tells me that they will use an ID from the processor to identify the source. I’m guessing that this information will be embedded in documents and multimedia files and probably encrypted and have a hash to detect changes. I’m guessing that there will need to be some external certificate authority as well to stop easy hacking of the provenance info.
Intel is the biggest single contributor to the Linux kernel, so the Linux kernel is likely to get support for this feature if it ever sees the light of day. However, it also won’t be hard for any Linux distro to strip out any provenance info from files. That is the advantage of FOSS, that you can change the code to remove any feature that you don’t want.
Without more details, it is hard to know whether this is something to be concerned about or not, but it doesn’t seem like it would be hard to opt out by stripping identifying info from files. I can’t see the two major parent distros (Debian and Arch) making it the default setting, so we probably are protected in the Linux world. However, I can foresee a future where you won’t be allowed to post files on certain platforms where the files don’t have provenance information included.
My recommendation is to use FOSS platforms where the major technical decisions are made by communities (like Debian, Arch, Gentoo, and their derivatives), rather than by commercial entities that have financial incentives to comply. If we have free/open source processors (like an OpenHW RISC-V processor in an FPGA), then it won’t be hard to modify the processor to not report identifying info.
My second recommendation is to call out misinformation when you see it and stop visiting sites which have a history of promoting misinformation, because you are helping to create the problem and giving fuel to initiatives like C2PA.