Compruebe expresa si el objeto está vacío
if(Object.keys(obj).length === 0) {
}
Fusinato
if(Object.keys(obj).length === 0) {
}//when this.state.errors object is empty
if (Object.keys(this.state.errors).length == 0) {
this.props.updateUser(user);
this.props.navigation.goBack();
}