Is it safe to use pine and poplar interior trim pieces together or will I have trouble later from things expanding/contracting differently in the future? Specifically, I have pine door jambs and would add poplar doorstop trim. Curious if poplar casing on pine door jambs would have issues too. I'm guessing most people wouldn't hesitate to do this but I am extra cautious about having pieces warp later on.
Every piece of wood will expand and contract at somewhat different rates. Even two pieces of pine from the same tree will likely be different.
Old furniture (like a chest of drawers) used to be made of oak or maple or mahogany, while the backs were often made of pine because it was cheap and nobody would see it. If these pieces have lasted for centuries, there's no reason your jambs and trim made of poplar and pine will have any issues.
As noted in a comment, though, you'll want to paint this, not stain it. Poplar isn't a particularly pretty wood for staining, but it's fantastic for painting.