Learn Russian: Мне всё равно, что он думает.

Всё равно literally means "all equal", and with a dative pronoun like мне it translates to "I don't care" or "it's all the same to me". However, it can also be used as a concessive particle meaning "anyway" or "all the same" (e.g., "he did it anyway"). It is often taught alongside всё-таки and всё же so you can contrast them: всё-таки means "nevertheless" or "still", but it can never be used to say "I don't care".

Why is мне in the dative case here instead of the nominative я?

The phrase всё равно forms an impersonal construction, similar to state-of-being words like холодно (cold) or надо (necessary). In Russian, you use the dative case to indicate the person who is experiencing that state. Literally, the sentence is saying "To me, everything is equal."

Is the comma before что strictly necessary?

Yes. In Russian, a subordinate clause (a dependent part of the sentence with its own subject and verb, like он думает) must always be separated from the main clause by a comma. While English seamlessly connects them without punctuation ("I don't care what he thinks"), Russian strictly requires the comma before что.

Is saying мне всё равно considered rude or aggressive?