Learn Italian: Lei critica una scelta qualunque, ovvero non rispetta nessuno. - She criticizes any random choice, that is, she doesn't respect anyone.

When qualunque comes before a noun (qualunque scelta), it simply means "any choice" or "whatever choice". But when placed after the noun with an indefinite article (una scelta qualunque), it takes on a dismissive tone, meaning "just any random choice" or "an ordinary choice".

Does ovvero just mean "or"?

It can, but in modern Italian it is most commonly used to mean "that is to say" or "in other words" (synonymous with cioè). Here, it clarifies that criticizing any random choice is equivalent to not respecting anyone.

How would the phrase change if we used the lesson's focus word, altrui, instead of qualunque?

If you wanted to say she criticizes "other people's choices", you would replace una scelta qualunque with le scelte altrui. Notice that altrui acts similarly in sentence structure: it is invariable and is placed strictly after the noun.

Why do we need non if nessuno already means "nobody"?

Italian requires a double negative when a negative pronoun like nessuno comes after the verb. If you moved it before the verb for emphasis (nessuno rispetta), the non would be dropped, but the standard phrasing is non rispetta nessuno.