In practice, this isn’t something that I have seen come up terribly often (not on here nor on the IRC channel). It is certainly something to keep in mind for extreme circumstances. Normally, it is considered best practice to run as new a kernel as possible.
I have seen at least one case where someone was trying to run very very old software inside a docker container: Help get JDK 1.0 working in Docker?
I don’t know if the trouble that they ran into was due to a kernel syscall incompatibility or another version mismatch issue. The fact that they got it working at all seems to suggest that modern kernels should be able to run older userspaces just fine.
Granted, my evidence is anecdotal. Someone more knowledgable about the linux kernel might be able to shed more light on this.