The mother is giving TV interviews and money is being raised by public crowdfunding.
They have an active FB group.
The family have not asked for privacy, they've courted publicity for the case, including sharing photos of the child in a nappy in hospital.
They've made serious accusations against the hospital and HCP's caring for Archie.
They've invited comment by the actions above, especially when trying to promote their cause they have made statements/allegations that on occasion have been untrue and contrary to the court records.
There is also a matter of public interest in how long it's ethical to maintain the body of a person who is brain dead. Most importantly re; the dignity of that person and frankly the scare resources it takes to do so that could be arguably better utilised elsewhere.