Do We Have to Obey Every Word of Muhammad (as)?
The obedience is not to the personality of the messenger. The obedience is only to the orders which the messenger brought from Allah.
The Quran orders obedience to the Rasul (Messenger) Muhammad not to the son of Abdullah, or the Nabi (Prophet) Muhammad (al-Ahzab  36)! A nabi is also followed only when he abides al-Maruf (the principles of the Quran) (al-Mumtahina  12).
Obedience to the Rasul (Messenger) is obedience to Allah (an-Nisa  80). Disobedience to the Rasul is rebellion against Allah (an-Nisa  14). Whoever disobeys the Rasul will be thrown into hell (an-Nisa  115). Those who upset the Rasul will be cursed in this world and hereafter (al-Ahzab  57).
It should not be forgotten that all these warnings are only about the Rasul (Messenger). In the Quran, examples are given about people who did not follow the Nabi (Prophet), but did not face any threat or sanction:
— Zayd did not obey the word of the Nabi and divorced Zaynab. However, as a result, it was not stated that he was a disbeliever (al-Ahzab  36-37).
— A group of believers argued with our Nabi, but they were not warned of any threat (al-Anfal  5-6).
— Some of the Companions upset our Nabi, but Allah did not threaten them with hell (al-Ahzab  53).
— Hawla argued with our Nabi, and she did not consent to his decision. But she was not declared a disbeliever (al-Mujadila  1).
— Some of the women of the Nabi objected to the Nabi (al-Tahrim  1-5). They were warned, but it was not stated that they were disbelievers.
Therefore, we have an obligation to obey only the commands that Muhammad (as) conveyed as a Rasul/messenger, not every word.