For something considered modern, pretty much next to impossible.
All of the modern CPUs require blobs to function, whether it's microcode, embedded firmware, binary driver blobs, or otherwise.
I don't believe there is a wireless card (wifi, Bluetooth, etc.) on the market that doesn't use binary, closed source firmware. In fact, it's almost mandated by law that there can't be. FCC regulations require that devices be made resistant to attempts to change their function in an effort to limit people's ability to transmit stuff unintentionally (or intentionally). Modern radio protocols are heavily dependent on SDR (software defined radio), so fixed function is probably infeasible. You could make the firmware unchangeable, but now any bugs discovered in your public source code are now entirely uncorrectable.
Heck, even the SDR community is having to be really careful about not drawing the ire of the FCC. That's why so few of them tend to advertise transmit capabilities.
The main ARM cores have been generally blob-less, but that's only the cores. Various SOCs require blobs to initialize. Their GPUs are all proprietary blobs up and down the stack.
So you basically would have to make your own GPU, your own radios, etc. and integrate them into your own SOC - and get the regulatory bodies to certify them for sale in their various countries. You then have to fight the entrenched companies in court over IP for years. The GPU portion will be especially tricky. The moment you try, lawyers from Nvidia, AMD, Imagination Technologies, Apple, etc. will be all over you. The radios will have Qualcomm, Broadcom, and Intel all over you.
So technical, legal, and regulatory hurdles - which is why I say next to impossible, especially on the FSF's budget.
- a jaded hobbyist