tc_acquire_table and tc_release_table are critical sections of table cache. Among other things, they update TABLE::in_use:
tc_acquire_table - table->in_use= current_thd
tc_release_table - table->in_use= 0

Normally table->in_use is only accessed/modified by thread that owns this table instance, which means access to this variable doesn't really need to be synchronized.

There are a few exception though when foreign threads may read this variable:

• TABLE_SHARE::visit_subgraph() (MDL deadlock detector): called after marking table(s) old and purging unused table instances, thus tc_acquire_table() must never change in_use (because there is nothing to acquire); tc_release_table() must be fixed not to change in_use while table is in all_tables list. Otherwise no synchronization needed.
• kill_delayed_threads_for_table(): mostly same as for TABLE_SHARE::visit_subgraph().
• list_open_tables(): no synchronization needed, unsafe access is acceptable.
• print_cached_tables() (debug only): synchronization needed.
• check_unused() (debug only): remove this function, it was supposed to check unused_tables, which was eliminated by MDEV-5388.
• tdc_remove_table() (debug only): no extra synchronization needed, protected by exclusive MDL.

There are a few options how we can synchronize access to this variable:

• mutex (can be complex, MDL deadlock detecter needs recursive lock)
• rwlock
• atomic spinlock (requires much less memory than mutex/rwlock)