In current glibc master, it's unsafe for any putenv/setenv to race with any getenv, even if the variable names are different, for two reasons. (Note that multiple calls to putenv/setenv are serialized by a lock, but getenv does not take the lock.)
(1) setenv resizes environ using realloc, which frees the old buffer, so getenv can end up reading from a freed array.
(2) The code does not use atomics or memory barriers, so on weakly ordered architectures, getenv could observe another thread's write to one of the pointers in the environ array, or to the environ pointer itself, while observing stale values for the memory behind it.
In both cases, getenv could end up returning a bogus pointer or just crashing.
However, those issues can be fixed without changing the API, and at least Apple's libc seems to do the right thing here. On the other hand, other libcs such as musl, FreeBSD libc, and even OpenBSD libc (!) do worse than glibc and have no locking at all.
If someone could convince the maintainers of all those libcs to add a lock and make getenv/setenv 'thread safe as long as you're not racing on the same variable name', then that would be a good starting point. But in my opinion it would still be a half-measure. We need a fully thread-safe environment.
And honestly, it might be easier to convince the maintainers to add a full solution than a half-measure, even if it involved API changes. (But it may be hard either way. Rich Felker showed up in a Rust thread a while back and was highly negative on the idea of making any changes to musl.)