Serial communication and parity bit
You may find contradictory answers because there are many kinds of serial communication protocols. Some are LSB first, some are MSB first.

For example, for the old RS232 standard and siblings, the LSB is transmitted first, and the parity may be transmitted after MSB. The MSB is usually the 7th bit or the 8th bit.
The parity is not part of the source data and is not weighted, so this is not really a MSB.

Another serial protocol, CAN, used in many automotive or other embedded applications, uses MSB first.

Some have more complex interpretations, mixing LSB- and MSB- first for data and CRC, mixing the order of bytes and the transmission order of bits. Example : IP over Ethernet : Big endian data, LSB-first bits, reversed CRC.