To my knowledge, legally they can not schedule outside my availability or terminate me for not working outside of my available schedule.
That knowledge would not be correct. Federal and state laws don't protect you for availability (disclosure: I am not an attorney). This is why unions exist (but let's not turn this into a pro or anti union discussion).
Since neither you nor Target signed a contract for employment conditions, they can schedule you for whenever they want. However, Target is supposed to (on the basis of internal policy — that is to say, "Scout's Honor") follow and adhere to your availability for the purpose of coverage. They can also play the "your availability no longer meets our needs so we're gonna have to let you go" card without anything you can do.
The flippant response by your leadership is alarming, but if you find it worth your time to pursue a solution, go up the chain. Officially discuss with your ETL (the person ultimately responsible for making your schedule in 99% of situations) and remind them of your availability and ask them to please respect it. If that fails, involve the ETL-HR or SD and have the same discussion.
It's important that these be conversations in a sit-down setting and not just in passing, for the next step. If possible, write them an email after your discussion where you matter-of-factly state the discussion you had, the concerns you discussed, and a recap of their response. You guessed it... a paper trail.
Because the last step, if nothing comes of this and you're still energized like the Energizer Bunny to keep going... you're gonna have to call the dreaded, last resort mythical thing we call the Compliance Hotline. And they want facts. And if you have a paper trail of the "okay, we'll do better" conversations with clear inaction on their part, Corporate will love it.
Good luck!! Not to sound condescending or anything, but in closing... you may want to start looking for employment elsewhere or transfer to another store if you've had these in-passing convos with them and nothing changed before. They're doing this to push you out via you giving up or them painting you into a corner by saying you're missing shifts or parts of shifts when they inevitably conflict with your other job.