Answer: In terms of authorizing an unaccompanied youth to go to a GED testing site or a community agency, the district should follow whatever the policy is for other activities for unaccompanied youth. Most districts let youth make decisions about enrollment, scheduling, leaving campus for a doctor visit, etc. on their own behalf. If that is your policy, then the district should follow the same policy for GED tests and referrals to community agencies.
Liability always is based on reasonable care and negligence. Whether you are working with a parent or a youth, that is always the basis for liability. The best protection is to exercise reasonable care— provide complete information to the parent/student about the health precautions in effect at the site and the best information you can share about risks, and let the parent/youth make the decision. If you send a youth to an indoor location where you know hundreds of students will be crammed in small spaces with no masks, no social distancing, and no other precautions, and you are requiring the youth to go, that potentially could give rise to a problem. But that does not seem to be the situation.
COVID-19 is a known risk that any reasonable person should understand at this point. We are not aware of any liability for referring a youth or family for optional in-person services, or even that an unaccompanied youth or parent has brought a lawsuit like that. The community agency and GED site might have slightly more of a liability risk, but again, only if they were being unreasonable in how they were accommodating people. If they are following basic guidelines of social distancing, masking, etc., there should be little to no risk.
For your McKinney-Vento students, personal protective equipment should be provided as needed.