If the President holds him or herself out as a mere servant of the political party who has elected him or her as President and not as a servant of all the people, it is difficult to argue that the office of the President should be respected because of the fact that the President also acts as the head of state.
Of course, it’s important to note that while the office of the President should ideally always be respected in a democracy, the individual who is elected to that office because of his or her political position can not automatically expect such respect as no politician can automatically expect to be respected merely for holding a certain office.)
But where a President suggests that politics (and the loyalty to a chosen party) trumps all, it is not only the person that is exposed to criticism and ridicule: it also becomes more difficult to argue that his or her office should not be ridiculed or mocked. This is because the person holding that office would have signalled that he or she does not hold the position as head of state in high regard and does not consider the office as important as holding the office of political party leader.