I'm trying to understand why Sunnis and Shias are so divided.
Is it because of the discussion after the death of Muhammad, or has it something to do with the rivalry between Saudi-Arabia and Iran that has been going on since the Iranian revolution? Follow-up; is that rivalry because of the sunni shia divide or something else?
The rivarly between Iran and Saudi Arabia goes back before the Revolution in Iran in 1979, back to the days of the Shah when Iran was a US ally and designated as the "policeman of the Persian Gulf". The Saudis and Arab nationalists resented Iran's dominant position in the Mideast and its close alliance with the US. Arab nationalists -- who incidentally were secular like Nasser -- and Saudis regularly bashed Iran under the Shah, who was also secular. That had nothing to do with Shia or Sunni
The significance of the Sunni Shia divide is overrated in the media; people who until yesterday insisted that "The Muslims" constituted a single, unified "Them" out to get "Us" have realized that Islam is divided into sect as is Christianity, and now seek to explain EVERYTHING as a result of a Sunni Shia conflict. Also, the Saudis have been promoting the idea of Iran as an expansionist Shia state out to undermine Sunni or "true" Islam. This suits their political agenda fine. The fact is that Shia don't necessarily automatically identify with Iran nor do Sunni with Saudi Arabia and in fact during the Iran-Iraq war, for example, the Shia of Iraq fought bravely against Shia Iran.
You might be interested in a previous answer I wrote on this question here: https://www.reddit.com/r/AskHistorians/comments/4x6588/when_did_the_fundamental_differences_between/
Happy to take any follow-ups as best as I can, I think it also addresses the contemporary political ramifications, at least as far as allowed by the 20 year rule.