You're correct. Most instruments that lack real time tuning capabilities use equal temperament tuning, which is a 20th century development.

Wind instruments are necessarily tuned to a specific key, due to the nature of the harmonic series. But most talented wind instrumentalists are capable of modifying pitch to be in tune in any key or chord.

Down the rabbit hole, read on at your own peril:

Even string instruments are tuned to a key, to a certain extent, due to the use of harmonics. It is possible to fine tune the pitch of a harmonic by shortening the string as usual, but it is exceedingly difficult, since shortening the string changes the position of the nodes (the spots on the string that must be touched in order to produce harmonics).