You may safely use any libgit2 object from any thread, though there may be issues depending on the cryptographic libraries libgit2 or its dependencies link to (more on this later). For libgit2 itself, provided you take the following into consideration you won't run into issues:
Use an object from a single thread at a time. Most data structures do not guard against concurrent access themselves. This is because they are rarely used in isolation and it makes more sense to synchronize access via a larger lock or similar mechanism.
There are some objects which are read-only/immutable and are thus safe to share across threads, such as references and configuration snapshots.
The error message is thread-local. The giterr_last() call must
happen on the same thread as the error in order to get the
message. Often this will be the case regardless, but if you use
something like the GCD
on Mac OS X (where code is executed on an arbitrary thread), the code
must make sure to retrieve the error code on the thread where the error
happened.
When built as a native Windows DLL, libgit2 uses WinCNG and WinHTTP, both of which are thread-safe. You do not need to do anything special.
When using libssh2 which itself uses WinCNG, there are no special steps necessary. If you are using a MinGW or similar environment where libssh2 uses OpenSSL or libgcrypt, then the general case affects you.
By default we use libcurl to perform the encryption. The system-provided libcurl uses SecureTransport, so no special steps are necessary. If you link against another libcurl (e.g. from homebrew) refer to the general case.
If the option to use libcurl was deactivated, the library makes use of CommonCrypto and SecureTransport for cryptographic support. These are thread-safe and you do not need to do anything special.
Note that libssh2 may still use OpenSSL itself. In that case, the general case still affects you if you use ssh.
If it's available, by default we use libcurl to provide HTTP tunneling support, which may be linked against a number of cryptographic libraries and has its own recommendations for thread safety.
If there are no alternative TLS implementations (currently only SecureTransport), libgit2 uses OpenSSL in order to use HTTPS as a transport. OpenSSL is thread-safe starting at version 1.1.0. If your copy of libgit2 is linked against that version, you do not need to take any further steps.
Older versions of OpenSSL are made to be thread-implementation agnostic, and the users of the library must set which locking function it should use. libgit2 cannot know what to set as the user of libgit2 may also be using OpenSSL independently and the locking settings must then live outside the lifetime of libgit2.
Even if libgit2 doesn't use OpenSSL directly, OpenSSL can still be used by libssh2 or libcurl depending on the configuration. If OpenSSL is used by more than one library, you only need to set up threading for OpenSSL once.
If libgit2 is linked against OpenSSL, it provides a last-resort convenience function
git_openssl_set_locking() (available in sys/openssl.h) to use the
platform-native mutex mechanisms to perform the locking, which you can use
if you do not want to use OpenSSL outside of libgit2, or you
know that libgit2 will outlive the rest of the operations. It is then not
safe to use OpenSSL multi-threaded after libgit2's shutdown function
has been called. Note git_openssl_set_locking() only works if
libgit2 uses OpenSSL directly - if OpenSSL is only used as a dependency
of libssh2 or libcurl as described above, git_openssl_set_locking() is a no-op.
If your programming language offers a package/bindings for OpenSSL, you should very strongly prefer to use that in order to set up locking, as they provide a level of coordination which is impossible when using this function.
See the OpenSSL documentation on threading for more details, and http://trac.libssh2.org/wiki/MultiThreading for a specific example of providing the threading callbacks.
libssh2 may be linked against OpenSSL or libgcrypt. If it uses OpenSSL, see the above paragraphs. If it uses libgcrypt, then you need to set up its locking before using it multi-threaded. libgit2 has no direct connection to libgcrypt and thus has no convenience functions for it (but libgcrypt has macros). Read libgcrypt's threading documentation for more information
It is your responsibility as an application author or packager to know what your dependencies are linked against and to take the appropriate steps to ensure the cryptographic libraries are thread-safe. We agree that this situation is far from ideal but at this time it is something the application authors need to deal with.