How can I safely drive a relay OR sense a switch from a single terminal?
It seems OK so far.  Initialization, intermittent cable connection or faults, not-considered.  ALthough you have not defined your max output current.  The port is rated at 25mA max and with your driver ... I assume is more than 25mA ? or 50mA? 100mA? 1A? for a 12V relay , SSR or ?

They have NCh arrays low RdsOn , not sure about Pch arrays

20V Pch 100 mΩ @ -2.5V cheaper if you buy 1k MOQ
https://www.digikey.ca/product-detail/en/diodes-incorporated/DMG2305UX-13/DMG2305UX-13DIDKR-ND/4251545  

I think you mean it to be XOR port (input  XOR Output). OR could cause contention.   ... like a R/W bus for status/control but not on the same time or same port.  Then it is simpler to ground switch for control ( low side). 

The port must never see > +/-0.2V outside rails to avoid shoot-thru failure.  So the 10K series current limits to the ESD diodes on all pins , OK. 

Therefore a 1N4001 relies on the 10k series to reduce the port voltage with internal Schottky diode protection. So it is OK.  BAT54 is an alternative.  

Simultaneous I/O

An alternative is to incorporate an external board wired in parallel for up to 2x 8 ports. Where the sensors (if connected) would also drive the relays using 5mA ( but not used)  This eliminates EMI from conducted coil spikes and makes radiated noise outside the box and also gives visual feedback with LED.

SMD OPTOCOUPLER isolation , driving ability , stable performance ; trigger current 5mA;   The module voltage is 5V, 9,12 V, 24V are available ; 
 

Now you have an "Inclusive" OR Relay with Opto Isolation and external wiring terminal block (also cheap). this means the sensor can drive the 5mA opto switch and Port Rx input at the same time or the relay can be driven by the Port Tx.  It also allows you choose independent hi or lo side control and allows you to expand to 16 ports.