The Alliance charter applies specifically to commanding officers and serving crew members and strictly prohibits fraternization on board Alliance vessels and in their away teams.That said, the Alliance Command is a very busy organization.
Should an agent decide to pursue romantic interests with certain crew members or allied agents, command will likely turn a blind eye, allowing the agent to lead a somewhat normal life despite the obvious pressures of being humanity’s potential savior.
Romantic subplots (considered sidequests) are controlled by creative dialogue choices with key characters, and as romances are kindled, they can also be abruptly cancelled by saying the wrong thing to the wrong person at the wrong time.
As such, agents who show generosity and compassion toward their squad members may be more successful in pursuing romances. Agents who are rash and rude to their squad may be very lonely indeed.
A male Shepard agent is able to actively pursue romantic subplots with Ashley Williams or Liara T’Soni. A female Shepard agent is able to pursue subplots with Kaidan Alenko or Liara T’Soni (Asari can mate with either sex of any species).