To summarise the comments by myself and @FumbleFingers:
Don't point! - An adult aggressively "squaring up" to another adult showing such disrespect probably wouldn't want to use this language since it's considered something one would say to a child i.e. "child-centric" language.
An exception would be if it was expressed in a roundabout way, such as
Who're you pointing the finger at? -Who are you blaming for this (as opposed to physically pointing)
"It's rude to point"
It's rude to point at something with your finger.
Both mean the same thing and are perfectly valid, the finger part is implied. Similarly, "It's rude to stare" (with your eyes is implied). As Fumble mentioned, you do need that "at/to" if you are going to include the something.
It's rude to point something out.
This option has a slightly difference meaning. Point is the action of pointing with your finger. Point out is when you notice something and mention it out loud, this may be accompanied by a pointed finger, but not necessarily.
He pointed out the house from a far just means he said:
Hey, look there is a house up head.
He may or may not also point to it, but the phrase means drawing your attention towards the thing, rather than literally pointing at it. I couldn't find any good definitions of this, but I hope it makes sense!