Views taxonomy terms page with two content types
Directly modifying the default "taxonomy/term/%" view is not a good option, you can clone the default view and can make the required changes to the cloned view.

The better solution for the above problem is the Taxonomy Display module. Taxonomy display lets you associate a vocabulary with a particular view. Now, when I click on particular term link, which is an alias for taxonomy/term/%, the view takes over and this is actually rendered correctly maintaining the integrity of the field structure.

The detailed documentation of taxonomy display module is available here.