Looking here, I see this:
The UART transmission is enabled by setting the UTXEN enable bit (UxSTA<10>). The actual transmission will not occur until the UxTXREG has been loaded with data and the baud rate generator has produced a shift clock, in accordance with the value in the register UxBRG. The transmission can also be started by first loading the UxTXREG register and the setting the UTXEN enable bit.
Clearing the UTXEN bit during a transmission will cause the transmission to be aborted and will reset the transmitter. As a result, the UxTX pin will revert to a high-impedance state.
[Bolding mine.]
I am not familiar with the PIC but it sounds to me like you should not be enabling and disabling the transmitter. The TX pin going High-Z will cause the input to the level converter to become floating which is probably the source of the framing errors.
I'd suggest enabling the transmitter during initialization and leaving it enabled. As long as you don't feed the UART a new transmit character, it should remain idle.
If you want to use interrupts, when the transmitter is idle, mask the interrupt instead of disabling the transmitter.