I believe this item is already on the list of things the Devs are looking into, but I'm not sure of feasibility or ETA.
However, I can offer a partial solution: the GM team.
Step one: Have the SG leader (the character with the red star) tell the person they are not welcome in the base, and ask them to leave. This falls under our rule of "if someone tells you to leave them alone, you must leave them alone". This extends to SG bases. In an RP environment, make sure this is expressed Out of Character.
Step two, assuming they refuse: The SG leader should send in a support request, and/or ping @ game master on discord. If someone is available, we can take action. Even if someone isn't available, we can investigate the incident and take necesary actions against the offending account.
I know this is not a perfect solution. Sometimes the SG leader or a GM may not be available to facilitate all of this. A non leader may still take these actions, however, we greatly prefer to only communicate with an SG's leader when dealing with SG issues.
I must emphasize that step one is VERY important. Entering your SG base and being mildly annoying or socially inept isn't breaking any rules. You have to tell them, under no uncertain circumstances, to leave you alone (and by extension, leave your base). Them not doing so IS breaking a rule, and is actionable.
But yes, a way for people to control who can enter or stay in their base would be a good tool to have!