The parallel port (at least in it's later implementations) actually supports DMA - I'm sure that data exfiltration via the parallel port is hard, but probably not impossible...
The parallel port controller can DMA, that lets the driver tell the port hey, send this buffer out to the port and let me know or read this many bytes into this buffer and let me know. It's not peripheral controlled DMA like with firewire or PCI.
You can absolutely exfiltrate data via the parallel port... that's why you attach printers or zip disks... it's just that it needs host participation.
It’s almost certainly impossible on modern systems. The southbridge which allowed DMA to parallel port was absorbed into PCH and slowly stripped of legacy LCP support by chipset and motherboard manufacturers.
If I were an evil person I would start a cable shop where I sell all kinds of cables. And based on who the customer is I would send them a real cable or one with a nice and free to them surprise extra payload.
Who is going to x-ray each and every cable they buy? And who keeps track of where they sourced what cable?
Fuck the NSA. I did start off with 'If I were an evil person'. If I were an even more evil person I would go to work for the NSA. But no worries, I'm not politically aligned with anything in the USA right now and saw the writing on the wall two decades ago.