The two systems are plumbed together because:
APU bleed air needs access to the crossbleed duct to reach the starter for each engine;and
The Wing Anti-ice system needs access to the crossbleed duct for symmetrical anti-icing on one engine.
This arrangement eliminates the need for a separate APU bleed line to each engine starter.
The BMC takes care of switching logic depending on overhead panel selections and whether engines or APU are running.
The pilot must take care not to use APU for WAI as it's a limitation in the FCOM (not hot enough) and also to select one pack off for single engine WAI 'on' operations (status page & FCOM).