Your question
Is the color of the house red? Or is it white?
"Or" is a conjunction, not an adverb, so it cannot join two independent clauses.
What should be used instead of "or"?
That's not quite right. Conjunctions, especially coordinating conjunctions (FANBOYS) very much can join independent clauses.
He's a student, but I'm a teacher. Do you want to go to the movies, or would you rather play a video game?
Also, you're referring to conjunctive adverbs. Regular adverbs don't join anything.
What you really seem to be asking is if it's okay to begin a sentence with a coordinating conjunction. Purists might say no, but many grammarians argue that it's perfectly acceptable. Grammarian opinion aside, you'll find it's widely done.
In my personal opinion, it's okay IF it's done well, and for a purpose, on a limited basis. However, I frequently see students abuse it. Last semester I had a student do this with just about every other sentence because he hyper-corrected after I discussed comma splices. He was unclear on comma usage with coordinating conjunctions, so he avoided the issue by using periods and beginning the next sentence with them. If it becomes distracting, then it's not okay.
I'm sure you'll find plenty of people who argue that it's never okay to begin a sentence with a coordinating conjunction.