XOR

{% if is_state('binary_sensor.gate_closed', 'off') and is_state('binary_sensor.gate_open', 'on') %}
closed
{% elif is_state('binary_sensor.gate_closed', 'on') and is_state('binary_sensor.gate_open', 'off') %}
open
{% elif is_state('binary_sensor.gate_closed', 'on') and is_state('binary_sensor.gate_open', 'on') %}
  {% if states.binary_sensor.gate_closed.last_changed > states.binary_sensor.gate_open.last_changed %}
    opening
  {% else %}
    closing
  {% endif %}
{% endif %}