Center tap split supply question
The load currents do not need to be balanced. If they're not, it just means that there will be increased current in the center tap (ground return).
The transformer needs to be symmetrical. Both halves of the transformer supply power to both regulators, on alternate half-cycles. However, it is not necessary for the regulators to have the same DC output voltages. They can indeed be different, but just be aware that the one with the lower output voltage will be dissipating more power for any given load current, since the input voltage is the same going into both regulators.