If the noise is from the outside, then you are doing something wrong. You must have a stable ground plane and a stable Vcc. And you should split the ground plane for any radio signals from the ground plane for the digital section, and only connect at a single point. And you should think about using EMI filters to limit the frequency allowed in/out of digital signals.

If the RF module is connected directly to the serial port, and is noisy, then you must check closer if the module is having good supply voltages and that the module and the processur is expected to run on the same voltages.

The UART gets trigged by the start bit. Then it will count time based on baudrate and number of configured bits. The receive interrupt on the other hand is first when it get to the stop bits. The UART will generate an error instead of a data byte if no stop bits are found, i.e. if it got trigged by a false start bit. With the stop bit(s) found, you may also get other transfer errors, possibly detectable as a parity error.

If you have problems with noise on the signals, you have to work harder. And possibly come back with a better description about your circuit.