Hmm... I don't see an _r version of the odbc driver. There is an _r version for the libmysqlclient driver.
NPX1601155 unixODBC # cat odbcinst.ini
[myodbc-5.1]
Description=MySQL ODBC myodbc-5.1.6 Driver
Driver=/usr/lib/libmyodbc5.so
UsageCount=1
NPX1601155 unixODBC # ls /usr/lib/libmy* -lah
-rwxr-xr-x 1 root root 297K Dec 10 08:48 /usr/lib/libmyodbc5-5.1.6.so
-rw-r--r-- 1 root root 465K Dec 10 08:48 /usr/lib/libmyodbc5.a
-rw-r--r-- 1 root root 1.1K Dec 10 08:48 /usr/lib/libmyodbc5.la
lrwxrwxrwx 1 root root 19 Dec 10 08:48 /usr/lib/libmyodbc5.so -> libmyodbc5-5.1.6.so
lrwxrwxrwx 1 root root 30 Dec 10 08:21 /usr/lib/libmysqlclient -> mysql/libmysqlclient.so.16.0.0
lrwxrwxrwx 1 root root 30 Dec 10 08:21 /usr/lib/libmysqlclient.so -> mysql/libmysqlclient.so.16.0.0
lrwxrwxrwx 1 root root 30 Dec 10 08:21 /usr/lib/libmysqlclient.so.16 -> mysql/libmysqlclient.so.16.0.0
lrwxrwxrwx 1 root root 30 Dec 10 08:21 /usr/lib/libmysqlclient.so.16.0 -> mysql/libmysqlclient.so.16.0.0
lrwxrwxrwx 1 root root 30 Dec 10 08:21 /usr/lib/libmysqlclient.so.16.0.0 -> mysql/libmysqlclient.so.16.0.0
lrwxrwxrwx 1 root root 32 Dec 10 08:21 /usr/lib/libmysqlclient_r -> mysql/libmysqlclient_r.so.16.0.0
lrwxrwxrwx 1 root root 32 Dec 10 08:21 /usr/lib/libmysqlclient_r.so -> mysql/libmysqlclient_r.so.16.0.0
lrwxrwxrwx 1 root root 32 Dec 10 08:21 /usr/lib/libmysqlclient_r.so.16 -> mysql/libmysqlclient_r.so.16.0.0
lrwxrwxrwx 1 root root 32 Dec 10 08:21 /usr/lib/libmysqlclient_r.so.16.0 -> mysql/libmysqlclient_r.so.16.0.0
lrwxrwxrwx 1 root root 32 Dec 10 08:21 /usr/lib/libmysqlclient_r.so.16.0.0 -> mysql/libmysqlclient_r.so.16.0.0