Is it rude to not dress up when your having guests for the holidays?

There is no hard and fast rule as it depends on the occasion and a person's background. If the birthdays, special occasions, etc. are extremely informal then casual attire is acceptable. Basketball shorts are kind of "iffy"and are more appropriate for playing games rather than a backyard barbeque.    If the occasion is special such as a more formal dinner party then it would be expected the host and hostess dress for the occasion. 

Being a slob doesn't know one geographical location over the other and my two friends from Kentucky are if anything TOO formal in the way they host events (literally, place cards at a last minute potluck picnic). But your sister apparently either doesn't see any problem with this or is just sick of arguing about it with him. It's certainly not the most polite thing in the world to be overly casual like that. However, if this guy's job involves a uniform and they don't regularly go to religious services he'd be less likely to even own suitable clothing. There are many people in this world who have to go buy a suit every time someone in their family dies because their wardrobe isn't expecting to ever have to look nice.

It's trashy to dress as he does but it's not rude in that it's not your problem and shouldn't be an inconvenience to you.  You're their guests, so be appreciative that they had you over. Dressing like that just makes him seem trashy and low-class.  It's not a Southern tradition to dress like that; it's slovenly.

I'm not quite sure what makes you feel like you're so self-important that people have to dress up for you. It is his house he can wear whatever the heck he wants.

He's not rude. He has the right to wear whatever he wants in his own home in front of company as long as anything that would need to be covered in public is covered.

His house - he can wear what ever he wants to wear.

So what?  You're there to socialize and enjoy the company.  Is he acting rude?  Is the place clean for guests?   They invited you to their house for the holidays!  That's their time, money and energy put in to having you as a guest.  Hello!?  Do you invite them to your house often?  Do you spend your own money entertaining them?  I bet not.  Entitled anyone?!  Thank them for the invite since you did take them up on it.

It's not rude, its his house and his body, so he makes the rules on what he's going to wear.

You're the one who is being rude. He has the right to dress as he pleases in his own home

He feels he is at his own home and wants to be comfortable. It is not nice, not to dress up when company cones over.