Is it permissible to write adhkar (remembrances of God) and tasbih (glorification of God) on a protective head covering with the intention of remembering God, given that there is an opinion that this diminishes the reverence due to the majestic word [Allah]?

The name of Allah should not be written on hats, in order to protect Allah's name from desecration and to relieve the wearer from embarrassment if he enters the lavatory. The aspect of desecration is that a hat is worn, taken off, placed on the ground, and can be subjected to harm. Furthermore, the wearer might commit something forbidden while the name of Allah is on it. Sheikh Ibn 'Uthaymeen said: "We have not found that the gathering where something from Allah's verses is written increases people's piety... rather, we see that in some of these gatherings, evil is committed: smoking takes place therein, people backbite therein... and the Book of Allah is above his head while he is engaged in disobedience to Allah."