Electronic – phase-shift oscillator design decisions

C1 to ground in series with the crystal and then another C2 to ground.

It's not obvious exactly what your circuit looks like, but to clarify my answer, I'll show you what imagine it looks like based on your description:

^{simulate this circuit – Schematic created using CircuitLab}

Incidentally, this circuit, with C1 in series with the crystal, is not what I think of as an especially common oscillator circuit.

If the RF signal is AC why doesnt the AC signal just go straight to ground?

The very simple description of a capacitor is "at low frequencies it's an open circuit and at high frequencies it's a short circuit." And this is a reasonable model for a lot of cases. But saying you have an AC signal doesn't mean you have a low or a high frequency, it just means the frequency is not exactly 0 Hz. And what's happening here is that the frequency you're operating at is neither a "low" frequency or a "high" frequency, it's somewhere in between.

Between the two extremes you need to look at the impedance model of the capacitor:

\$Z = \dfrac{1}{j2\pi{}fC}\$

This also tells you what is meant by "low" and "high" frequencies. When the frequency is low enough that Z is so large it doesn't affect your circuit differently than an open circuit would, that's a "low" frequency. When the frequency is high enough that it doesn't affect your circuit differently than a short circuit would, that's a "high" frequency.

Without capacitors how can you expect the crystal to produce a phase shift of 180 degrees at its resonance. There needs to be 180 degrees of phase shift because you need a total of 360 degrees and the inverter provides only 180 degrees hence it's called an inverter.

If you want to read more try this - it's quite a good document on the subject by Microchip entitled AN826 Crystal oscillator basics.

Here is also a very good article about figuring out the series resonant point and the parallel resonant point (all xtals have them and this basically determines the capacitor values chosen.