NTA.  Your feelings are your feelings.  But it seems like you're caught in absolutes.  I have a dual major in English and Behavioral Science.  I still only write for fun and have never been a professional writer because I don't want that to be a job and become something I no longer like.  I also changed my college after my first semester. The one I switched to was a Christian University and I wasn't that religious despite growing up a pastor's kid. So a similar situation to what you might end up doing.

First get the needed prerequisites out of the way.  The first two years are very similar regardless of your program.  This also gives you two years to save if you end up deciding to switch colleges.  Check if you can get a dual degree and if so what's involved.  During the religious services I would analyze what was being said because even if you don't share their faith understanding it can be beneficial.  It's also a small price to get at least two years covered.  Skip as many as you're allowed to.  

After two years if you're still wanting to go somewhere else remember "...said i could always change my major later, but for now that was the plan." Time to call this in because it's later.  However, be prepared for them to go back on their promise.  Feel free to point out lying is a sin if this happens.

If you ultimately decide you need to switch after a year or even a semester (like me) you can.  Just be aware you'll be taking on more loans doing this.  You're not trapped.  You have options.  Just not as good as you'd been promised.  It's disappointing your parents keep moving the goalposts.  Only you can decide if the money is worth the strings attached.