Pull-up resistors needed for quasi-bidirectional push-pull PCF8575/PCF8574(A)
The only real need for pull-ups would be to ensure that either the output starts or goes high when the output is not driven or to force the pin into a particular state when the pin has an open input.

The spec sheet says "At power on, the I/Os are high. In this mode,
only a current source (IOH) to VCC is active." That is, the maker already thought of that for you, assuming you don't need it to start out low....

However, if your particular design needs to hold a particular pin in some state while you switch it around, that is another matter.