Hi Tonlee,
I am having a HP Deskjet D1500 series printer. It works like charm with
Trisquel GNU/Linux 6.0.1 LTS version. So I understand, atleast from software
point of view, the HP Printers of D1500 series are completely compatible with
free software. But the same may not be true for some latest models of HP.(You
need to check it with your local HP vendor)
Now coming to Hardware, it cannot be affirmated a Hardware which supports a
free distribution to be 100% free; Reverse engineering the Technical
schematics/Hardware Description code of the product(Here your Printer) with
the permission of the company, alone can prove it indeed free.
It can also be a possibility that a hardware that can work for a free
distribution can also have non-free firmware blobs. So it would be wise to
avoid using such a suspected device for communicating sensitive/private data.