The standard way to ask a question in English is Do you [verb].
Do you want to have a pizza? Or not?
Do you want to have a pizza, or not?
If you chose to not use Do you as the regular form of question, this usually implies either that you know the person well and maybe that you have been having a longer conversation up to the point when the question is asked.
Want to have a pizza, or not?
Want to have a pizza or not?
Dropping off the Do you is informal but most of all implies you are already in a conversation or hanging around with a person when you ask the question. So, it can be seen as rude if you ask a question without it.
Often, with children who have been making a ruckus, a parent might leave off the Do you in asking the question. In that sense, it is almost a threat meaning: If you [the child] do not start behaving well, you can't have a pizza. So, it can also denote annoyance or irritation. Couples when annoyed with each other might also leave off the Do you. Also, good friends might leave it off because they know each other well and in that case, it is merely informal.
The or not is neither rude nor not rude.