Once you place tefillin into a specially made bag for the first time, that bag comes under the category of tasmish kedusha and may no longer be used for mundane purposes such as keeping coins in it. (ShA3)
You are able to make a condition that limits the kedusha of the tefillin bag. When making the bag, make a condition that you should be able to switch the use of the bag to any mundane (but not disgraceful) purpose. (Rama 3 – MB17)
You are allowed to use a tallis bag for mundane purposes even if you keep your tefillin bag in it. (MB11)