Is it legal to walk into someone else's house if the door is unlocked?

Not without permission, it's not. In every jurisdiction, entering a residence that is not yours or that you are not a tenant of through an unlocked door (or an opening or crawling through a window that’s partially opened) is a crime if one doesn't have permission to be there, thus constituting both "trespassing" and "breaking and entering," the word "breaking" being a bit misleading for some since the crime of "breaking and entering" actually requires no physical force of prying, kicking, or other damage to transpire. "Breaking and entering" is also a separate charge from burglary, and you can be charged for it even if you committed no other crime.

Don't do that in a red state .

Of course it is not.  

Entering anyone’s house or property without permission is unlawful, defined as trespassing.  That’s all that is required. Most jurisdictions have that as a misdemeanor.  If an intent to commit any crime whatsoever can be described, it becomes burglary.  That’s a felony.

It’s also important to note that some states have enshrined the “Castle Doctrine” in their laws.  That (pretty much) means a homeowner can use deadly force without retreating the moment your big toe touches their property line.

It's liable to get you a gut full of buckshot, or, if you're lucky, rock salt

yess now poop oon the floor and claim your territory

Of course that's not legal and why would you want to do that anyway?