Can the editing capability of a public hosted feature layer be assigned to specific members in ArcGIS Online?

No, it is not possible. In most cases, when sharing a hosted feature layer with the public, the editing capability of the layer is disabled, and if disabled, only the owner of the hosted feature layer or the organization's administrator can edit the layer or table layer's contents.

The editing capability can be enabled for other members, however, if enabled, there is no access restriction to the hosted feature layer. Everyone, including anonymous users, have access to change, delete, or edit the data, so enabling this capability for a publicly shared hosted feature layer is not recommended.

Alternatively, provided below are two workflows to edit the public hosted feature layer without enabling the layer's editing capability.

Create a shared update group

A shared update group is useful for multiple people to update the same item in an organization without enabling the hosted feature layer's editing capability. Members of the group are assigned privileges to edit the contents of the hosted feature layer, alter the editor tracking settings, and enable or disable attachments. In ArcGIS Online, create a shared update group and add the public hosted feature layer to the group. In Group designations, enable the Shared update option. Refer to ArcGIS Online: Create a group for instructions to create a group.

Note:
Ensure the role of the members added to the group is User, Publisher, or Administrator.

Create a hosted feature layer view

A hosted feature layer view is a view of the data in the source layer (hosted feature layer) where edits made to the layer are displayed in the layer view. The editing capability of the hosted feature layer view is not inherited from the hosted feature layer, so, the editing capability of the view layer can be enabled even though the hosted feature layer's editing capability is disabled. Refer to ArcGIS Online: Hosted feature layer view settings for more information. In ArcGIS Online, create a hosted feature layer view of the public hosted feature layer and enable the editing capability of the layer view. Refer to ArcGIS Online: Create hosted feature layer views and ArcGIS Online: Enable editing and configure the types of edits that are allowed for instructions.