I don't know if this is the proper way but it works for Odoo 12.

Now you can add the attribute hide_to with the name of the group in the oe_chatter div (You also need to replace * with div tag in `appendTo($('*'))` )



// in your xml add this attribute to the oe_chatter div: 
// hide_to="your_module.your_group"


odoo.define('custom_widgets.chatter', function (require) {    
"use strict";

const Chatter = require('mail.Chatter');    
const FormRenderer = require('web.FormRenderer');    
const Session = require('web.session');

FormRenderer.include({        
    _renderNode: function (node) {
        if (node.tag === 'div' && node.attrs.class === 'oe_chatter') {
        const disable_attachment_box = this._disableAttachmentBox(node.attrs)
        if (!this.chatter) {
            this.chatter = new Chatter(this, this.state, this.mailFields, {                        
            isEditable: this.activeActions.edit,                        
            viewType: 'form',                        
            disable_attachment_box: disable_attachment_box,
        });                    
        this.chatter.appendTo($('*'));
        this._handleAttributes(this.chatter.$el, node);
        } else {  this.chatter.update(this.state); }                
        return this.chatter.$el;            
    }  else {                
        return this._super.apply(this, arguments);            
    }        
},          
_checkGroup: function (group) {            
return Session.user_has_group(group).then((res) => { return res });        
},        
_disableAttachmentBox: function (attrs) {            
    const disable = 'disable_attachment_box' in attrs;
    if ("hide_to" in attrs && attrs.hide_to)                 
        return disable || this._checkGroup(attrs.hide_to); 
    else return disable       
}    
});
});