Not every Intel... you should be safe if you use a Core2Duo, but only if you Libreboot it, which means you will need to do hardware changes unless you buy one that is directly modified by someone you can trust. There are some Laptops like the Thinkpad x60 which only require you to flash the bios and do some changes without modifying the hardware.
If you want it to be ME free by default, you have to go as back as Pentium 4...
With AMD, you have PSP, so it's the same, and you can't disable it, we know less about the PSP than the ME. You would need to back in time too, I think 2013 was the last year it was PSP free. Still faster than a Raspberry.
There are some workaround against IME, and Purism and System76 sell laptops with the IME disabled. They all have Intel laptops, though, not sure how things look with AMD.
Purism aren't safe.. it's an overpriced gimmick. You can't disable IME with the modern CPU's that are used in Purism laptops. It's a workaround with Coreboot but you still have Intel's propietary binary blobs. There's no workaround, you need old hardware, and you need to do the hardware changes I said, if you want to use Intel and be as private as possible. You need Libreboot, not Coreboot, and thus you are limited to a very small array of hardware. Same applies for System76. They are using i5s and i7s.
With AMD there's nothing to do, other than buying older hardware.