The wiring is not symmetrical.
However most phone systems are indifferent to the polarity of the line. Some older PABX and enhanced PSTN systems did require the correct polarity before enhanced functions would operate. The bulk of modern electronic phone line termination circuits incorporate a bridge rectifier before the DC clamping/hook/flash circuits so do not know which polarity is connected.
10 and 100 Mbps UTP LAN cabling makes use of a RJ45 8pin connection. Only 4 of the circuits are used even if all 8 are connected. The pinout requires the transmit pins of one device to connect to the receive pins of the other device. This requires proper pin selection. The transmission is a differential drive so the transmitter has a positive and a negative pin and these must match the appropriate positive and negative on the receive side. The LAN interfaces were made with the transmit either on pins 1 and 2 and receive on pins 3 and 6 but on devices like network switches and hubs the transmit was on 3 and 6 and receive on 1 and 2. This allowed straight through cabling in this standard configuration. The cable pairs had to be on 1 and 2 and the other on 3 and 6.
Now when there were more unusual connections cross over cables were required. All this was a bit confusing so automatic detection of which pairs were connected to which pins was implemented. Modern devices appear to also tolerate crossing of positive and negative as well as swapping of pairs.
Modern Gigabit LAN uses 4 pairs and does not need cross over cables as it establishes the wiring in the hardware and communicates appropriately. I am not certain if the standard requires them to ignore pair crossing but this may be possible.
So the answer to the LAN question is modern systems also seem to be increasingly indifferent.