Using Capacitors on a PCB
Without more details on the capacitor specifications we can just speculate on the exact reasons, however there is one problem that clearly jumps out. 

Technically speaking, your power traces are crappy. Their resistance and inductance would be too high for a power supply trace.  This introduces power droops and ringing into the system. 

If you have too good of a capacitor (low ESR) ringing will become a problem (this could be why tantalum is worse) and, regardless of the capacitor type, the thin segments of trace between it and the connector will introduce inductive and resistive droops in the power supply. 

Add some wire between the connector and the capacitor to reduce trace impedance and start from there



Oh, and regarding that stalling line of code. If the power distribution to your microcontroller is as bad as in that small section you posted, it’s very likely that power to it is dropping too much when the RF transmitter turns on.