My friend according to my personal belief you do not get convinced by reasons, its actually from the Guidiance of God almighty
Regarding the prophets, we are a people who like to follow the footsteps of the prophets in the ceremonial laws, and daily life activities, since the prophets were send to us as perfect examples on how we should live our lives, we should follow them to the fullest.
I will elaborate on this part, but please first tell me about your background which country are you from. See, in generally asia or in many countries, no non-muslim girl would prefer a beard person over a non beard person as his boyfriend so by keeping the beard he has boy cotted himself from such oppurtunities to sin. when he person keeps a beard he will always be mentally bound by the beard see i have a beard i know everytime, i am planning to do something bad it comes in my mind that i have a beard and yet i am doing something bad, if others see me then they will think every muslim is like that so we avoid sins,
It is a fard for every muslim to greet another one even if they are strangers and had never met, the person who greets first is better. thats why you can see in many of our muslim threads every new guy comes and there is a salam, so if there is no identity naturally no one will follow this habbit. because people will think oh he might be a hindu or a sikh and might get offended. like in the UK, this habbit has died out. but when we go to a muslim country there are full of greetings.
If you say Salam alekum to a muslim, it is also Fard (obligatory) for him to return the Salam. how can you sin by greeting a non-muslim. greetings is supposed to be a good thing, the concept of sin only arise if you do something bad. regarding this some hardcore Pakistani scholars do give different fatwas. but Prophet Ibraheem said Salam to his idol worshipper Father and said i will pray for you when his father kicked him out.
I hope if i had answered your questions, All praises is God Almighty the all seeing and all knowing