No such thing as stress in tarantulas...they dont feel emotions. What they are is uncomfortable in there environment/situation.
I am guessing by emotion you mean a conscious feeling. At risk of turning too philosophical I 'feel' like seeing as science doesn't understand consciousness in humans and how it is formed, there's no way we understand this in tarantulas with so little research on them, or know how much they 'feel' or what that even means for them. Personally I think both consciousness and feeling is a continuum and all we can assert is that tarantulas have far 'less' of that than us, or mammals, but we don't know how much less or how to measure when it has crossed into nothing.
For the purposes of being ethical and not causing harm I feel like it's safer for people to assume that the tarantula does feel something, even if this is one day proven wrong or we re-define feeling. So I personally don't have a problem with the term 'stress' being used in reference to tarantulas. The aim of using that term ends up the same: try to make it more comfortable/ less stressed. I would be scared that people may interpret 'no feeling, no stress' as meaning it doesn't matter what you do to the tarantula as it doesn't feel anything anyway.
Can something be uncomfortable without feeling it?