Though Postgres provides nonblocking read/write access to table data, nonblocking read/write access is not currently offered for every index access method implemented in Postgres.
The various index types are handled as follows:
Share/exclusive index-level locks are used for read/write access. Locks are released after statement is done.
Share/exclusive page-level locks are used for read/write access. Locks are released after page is processed.
Page-level locks provide better concurrency than index-level ones but are subject to deadlocks.
Short-term share/exclusive page-level locks are used for read/write access. Locks are released immediately after each index tuple is fetched/inserted.
Btree indices provide the highest concurrency without deadlock conditions.
In short, btree indices are the recommended index type for concurrent applications.
Read the upstream documentation. For corrections, first check the current manual.