AC Analysis of emitter circuit, why can I ignore resistance R1 but not Rc?
A resistor that comes in parallel with a voltage source has effectively nothing to do with the rest of the circuit and can safely be ignored. See the following circuits that are equivalent:



In your circuit since you have vi in parallel with R1||R2 you can ignore R1||R2 as it doesn't matter to the circuit. However, if the signal source has some non-zero impedance, say Rs, you could no longer ignore R1||R2, as this in parallel with \$R_B=r_\pi + (\beta+1)R_E\$, makes a resistive divider at the base with the net effect that it decreases the voltage gain of the circuit as a fraction of \$\frac{R_1||R_2||R_B}{R_1||R_2||R_B+R_S}\$.