If you are a 17 year-old in foster care, then enlist in the National Guard, does that mean you no longer allowed in the foster care system?

That depends on your Foster Care Program, which is usually established by your county.  (Some states might have state-administered programs or state-wide policies addressing this particular eligibility question.)  Different counties could have different rules about that, so check your county foster care website.

You CAN'T enlist at 17 without permission from your legal guardian. Foster parents CAN'T grant such permission.

Correct.  You would be emancipated.  Which means getting a job or enrolling in college and paying for all expenses yourself.

You’d be far better off enlisting Active Duty

Boy am I glad I'm not a 17 year old