As Norvald wrote in his recent post:
A long time ago, libmysqlclient came in two versions: one that was thread safe and one that wasn’t. But that was a long time ago. Since MySQL 5.5, the thread safe libmysqlclient_r library has just been a symlink to the libmysqlclient library, which has been thread safe at least since then.
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Source: mysqlserverteam.com