How do I check whether my current super fund is Shariah compliant?

Four documents or fields answer it, and they are the same four InvestHAQ displays for every fund it tracks.

• The PDS - what the investment option actually invests in
• The holdings disclosure - APRA-regulated funds publish portfolio holdings; look for conventional banks and interest-bearing securities
• The named screening standard - AAOIFI, an index methodology, or in-house
• The Shariah board or adviser, and a current fund-level certificate

If a fund does not name a standard or a board anywhere in its disclosure, that absence is itself the answer to your question.