After being poked by CHOICE and eventually apologising for locking out third-party ink cartridges for use with its printers, HP has — as promised — released updated firmware for affected devices which should disable the block.
If you'd like to grab the update, you'll need to track down the proper download page on HP's driver site. While there's no guarantee firmware will be available for your particular model, gHacks' Martin Brinkmann was able to test the update on a number of HP printers, confirming that it did work for his hardware.
Brinkmann also recommends disabling any automatic updates you might have configured for your printer. It's a straight-forward procedure and HP has details on the process on its support site.
In this day and age, it's hard to believe HP thought the block would go unnoticed, or the backlash would be minimal. That said, I doubt this will have a massive impact on the company's bottom line in the long run.