What is the general procedure for matching networks when there are multiple circuits are connected back to back?
You need to match impedance between each block and between the antennas and blocks (every connection in the diagram). As long as you do that, the impedance of block1+block2+antenna will be equal to the nominal terminal impedance of block1 itself. In this case, you can design matching networks for each connection based on the nominal impedances. However, if you omit one of the matching networks, the effective terminal impedance of block1 will no longer be equal to the nominal impedance because of reflections from block2 and antenna, and indeed it will be difficult to calculate. So matching at each connection is the universal practice of RF engineers.