How does a buffer make the second segment of sequential filters not draw any current?

An ideal buffer is a device that has infinite input impedance and zero output impedance (if it has unity gain, it doesn't change any amplitudes). If you insert a buffer between the two sections of a sequential filter, from the point of view of section 1 of the sequential filters on the left: the buffer device looks like it has infinite $Z_{\rm in}$ and doesn't draw any current from section 1. From the point of view of section 2 on the right: section 2 sees zero impedance from section 1 (section 1's output impedance looks like zero) and it can draw as much current as it likes (as if it were seeing the AC voltage source directly), without affecting what goes on in section 1. So if section 1 and section 2 are separated by a buffer, their transfer functions can be applied sequentially, i.e., as a product $H_{\rm tot} = H_1 \cdot H_2$.