Cross-contamination just does not matter...IF and only IF...The food will be cooked. Example...You are making Chicken Soup. You gather all the ingredient, cut up a whole bird, onions, carrots and celery on the same board, same knife. Is there a safety issue? NO. While true that the veggies have been contaminated with Salmonella, who cares! It's all going in the pot for a 3 hour simmer at 190.
Most cheapo Hot Dogs are made of a mix of Beef, Pork and Chicken. You think these meats are stored and processed in separate rooms, on separate equipment? NO...One line to grind, season, mix, stuff and cook. Cross-contaminated RAW Wheenies? Yes but again, they will be cooked so no issues.
With all do respect to Pops, same applies to Brining mixed meats. The cross-contamination occurrs but it just don't matter...All the meat will be Cooked to internal temps of 145°F, Ham or Canadian Bacon, or higher. At an IT of 145 held 9.2 minutes, a far shorter rest than anyone gives, the Salmonella on or even IN injected and Brined Pork, Chicken or Beef has a 7log reduction, that's only ONE bacteria cell in a 10 million sample is still alive. Nothing that can hurt you. Add the bacterial growth inhibiting or straight out Killing effect of Salt and Cure in a Brine and, what is there to worry about? There are a ton of threads on the subject, all over the web, that say " Don't mix because of cross-contamination " and when challenged the answer is, " Better Safe than sorry..." Bottom line...There is not a single SAFETY issue mixing meats in a brine. I hope this helps...JJ