No one's answering, so I will.

If you put out food for birds, there is really little to do to restrict which species comes to your offerings.

Bluebirds and Mockingbirds do not eat the seeds that cardinals and finches do; hopefully you have berry producing bushes and trees that attract and feed them.

You can try to offer safflower, which I understand cardinals love, and no one else does. But even then, other birds may develop a taste for safflower.

Consider planting native flowers that produce seeds that birds will eat, as well as other natural foods.

Good luck.

(I'm sure I will be corrected here : )