It's quite common for companies to have a policy on grooming and presentation etc. Some enforce it, others not so much. I used to work for a music/dvd chain who were super strict. No tatts, piercings, crazy hair...male employees weren't allowed to have any kind of facial hair, they were very particular about the presentation of their staff. At the end of the day if you want the job badly enough you'll do what's asked of you.

I think it's a bit rich of them to ask your DP to come up to Sydney at his own expense, but as someone else pointed out Aldi is run very cheaply. To me it sounds like a way to see how interested he is in the job, hell I'd do it. Sometimes you have to stick your neck out a bit to get places. In the end it'll be worth it, Aldi pay their management pretty well.