Why don't chicken and turkey sausages typically have sodium nitrate, but other meat sausages do? It's just something I've noticed while shopping. All of the chicken and turkey sausages I've seen (across multiple brands) do not contain sodium nitrate, but all beef- and pork-based sausage always has sodium nitrate.

I vaguely understand the role of nitrates in the food safety of cured meats, but I'm wondering what is it specifically about turkey and chicken that don't require nitrates.
Check this essay: Time-dependent depletion of nitrite in pork/beef and chicken meat products and its effect on nitrite intake estimation  

Check the Figure.1, while preserving meat in long days, the nitrite content in chicken sausage is much higher than pork/beef sausage.
For food safety, Nitrosamine where is transformed from nitrite is an important cancer factor. So there are only pork/beef(red meat) sausage in market but not for turkey/fish(white meat).