There really isn't a whole lot of shifting going on on the autoX course, and I know plenty of people with ATXs in their cars and have never heard a single thing about wear issues. I usually tell people to just stick it in 2 and leave it, as you should be a lot more concerned with the steering wheel and the 2 pedals you DO have... And as far as being rough on the tranny, the best runs are going to come with being smooth and progressive with the controls anyway. If you are stabbing at the brake and gas, and making your tranny work really hard, then you aren't doing it right in the first place...
For example, on an average 60 second course, I might only be hard on the gas or brake about 5-10 seconds total. The rest of the time I am either setting up for, or driving through a turn, where heavy gas or braking would break my momentum or put me off line. It's actually a lot easier on the car than it seems..
I would encourage switching the tranny fluid for something better, as it's a cheap change that won't affect your class and certainly cannot hurt. However, I do not think that it's anything that you should be concerned about either.
Head out to the first event with your dad and both have a go. Let him experience it first-hand and then decide if it's still an issue he is concerned about. I think after experiencing it, he won't have any more worries.
Don't waste another minute waiting on parts, or anything else. Just get out there and start racing! You will suck at first, and you will be slower than many other cars, but the only thing you will regret is not starting earlier...