Questions: Salaam ul aikum,
Q. Could you elaborate on the Sunnah and benefits of covering one’s head with a hat, topi, etc. for a man?
Jazakullah khair.
Q. Is there proof that hat wearing is not a cultural tradition and is part of religion?

Q. Why do some people remove topi (hat) when going to the restroom?
A. The greatest benefit for Muslims to wear the hat is that it is part of the blessed sunnah. Doing things linked to the sunnah makes Allah happy. Allah (subhanahu wa ta’ala) being happy brings tranquility into our lives. Allah (subhanahu wa ta’ala) states:

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Say, (O Muhammad sallallaahu alayhi wa sallam) to humankind: If you love Allah, follow me (meaning the sunnah); Allah (in turn) will love you and forgive you all, (forgive) your sins. Allah is Most Forgiving, Most Merciful. (3:31)

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Say: Obey Allah and the messenger. But if they (the people) turn away, then verily Allah does not love the disbelievers (3:32)

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Whosoever obeys the Messenger (by following his lifestyle), has indeed obeyed Allah (4:80)

The Islamic type of hat or head covering (like that of a scarf for woman) also helps distinguish a Muslim from their counterparts. Contributes to making a person more proud of their religion, behaviorally makes a person more aware of responsibilities and less inclined to sin. An Islamic head cover would also add for a person to be more responsible in their interactions with fellow humans and create a higher level of accountability.

The uluma have been unanimous in that a person should wear a head covering prior to removing waste products from their bodies, and whilst performing salaah. Sadly, people tend to do the opposite; they think that because a hat is part of sunnah, it should not be worn in the bathroom. This is wrongful thinking.

As far as salaah, many feel pressured to do like those around them. Because they see others not wearing a hat, many choose to not wear it, or feel a stigma associated with wearing the hat. ‘Others’ negating a sunnah should not cause for us to do likewise. This is poor justification.

Pious men through the centuries have worn it. People attempting to emulate the pious have also continually worn it and continue up to wear the hat up to this day.
A2) Wearing a hat is not limited to ‘culture.’ Wearing a hat is a religious function. The type of hat can differ, so long as it does not emulate another religion, culture, fad or fashion.

Sayyidina Aisha (RA) reports that that when Rasulullah (sallallaahu alayhi wa sallam) was on a on journey, he would wear a hat with ear-flaps. While at home, Rasulullah (sallallaahu alayhi wa sallam) would wear a Syrian Hat. (Akhlaaqun-Nabi page104)

Habib ibn Salih (RA) narrates that when Rasulullah (sallallaahu alayhi wa sallam) would enter the restroom, he wore shoes and covered his head. (Bayhaqi volume1 page 96)

Hassan Basri (May Allah shower mercy upon him) states that the people used to make Sajda (prostrate) upon their turbans and hats. (People here is referred to the sahaba, those that tried to emulate Rasulullah (sallallaahu alayhi wa sallam) in their actions) (Bukhari)

Sayyidina Waail ibn Hujr (RA) reports that he performed Salaat with Rasulullah (sallallaahu alayhi wa sallam)and the Sahaaba were wearing barnases (hooded like hats). (ibn Khuzayma page 233)

Sayyidinah Ibn Umar (RA) says, Rasulullah (sallallaahu alayhi wa sallam)would wear a white hat (Majma-uz-zawaaid volume5 page 21)
Sayidinah Abu Kabsha (RA)narrates that the caps of the companions of Rasulullah (sallallaahu alayhi wa sallam) used to be round and spacious. (Mirqaat vol.8 pg.246)

Final analysis:
Hat wearing is part of sunnah. To liven a dying sunnah is greatly rewarding, more-so at a time when people attack it, or downplay its significance. Although not wearing a hat does not constitute a sin, wearing it when one has a choice to do so is rewarding. Trivializing a sunnah does constitute a sin. Hat-wearing is not merely a cultural thing, although other cultures do wear it as well. Wearing the hat in accordance with the sunnah would be part of Islamic culture, and religiously rewarding.

Allah certainly knows best.