Finally, here is the response that I got from Subaru of America on this topic.
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Thank you for taking the time to contact us. Subaru of America does not recommend synthetic gear oil for the transmission or rear differential in your 2005 WRX Wagon. This is because we have not tested synthetic gear oil in our vehicles. It is not that we are stating that it would cause a problem; it is just that we cannot state that it will not cause a problem.
If you were to use synthetic gear oil in your WRX, your warranty would not be automatically voided. However, any problems caused by synthetic gear oil would not be covered by your warranty, as again we have not tested this and cannot recommend it.
Thank you for the opportunity to be of assistance. If you need any future assistance, please feel free to contact us again.