i'll crash in to give the unpopular take on this,
the Prophet pbuh gave this as an advice to his followers so that they are different and have a unique identity from the others.
he mentioned that first before saying grow your beards and trim your moustaches,
this indicates that it was a solution to the problem, i quote the hadith along with another:
Narrated Nafi': "Ibn Umar said, The Prophet said, 'Do the opposite of what the pagans do. Keep the beards and cut the moustaches short.'
Whenever Ibn 'Umar performed the Hajj or 'Umra, he used to hold his beard with his hand and cut whatever moustaches. Ibn Umar used to cut his moustache so short that the whiteness of his skin (above the upper lip) was visible, and he used to cut (the hair) between his moustaches and his beard. (Translation of Sahih Bukhari, Dress, Volume 7, Book 72, Number 780)"
Narrated Abu Huraira: "Allah's Apostle said, 'The Jews and the Christians do not dye (their grey hair), so you shall do the opposite of what they do (i.e. dye your grey hair and beards).' (Translation of Sahih Bukhari, Virtues and Merits of the Prophet (pbuh) and his Companions, Volume 4, Book 56, Number 668)"
the closest companions of the Prophet (pbuh) usually understood the Prophet pbuh best, and made ijtihad accordingly.
it is on record that Caliph 'Umar (ra) had a long moustache that he would twirl when he got angry or agitated.
some Muslims, like myself tend to grow a trimmed beard, and it doesn't stop people from passing by me and greeting me with peace and shaking my hand.
some companions have taken this literally as can be seen from the first hadith mentioning Ibn 'Umar ('Caliph 'Umar's son).
who was very strict in following by the letter, other companions did however look at the context as can be seen from the march to banu Quraydhah and the command to not pray 'Asr until they reached Quraydhah,
some took it literally and didnt pray, some said that the Prophet (pbuh) was emphasizing the urgency and the need to make haste,
the prophet pbuh disapproved of none.
some companions were very strict in following the letter to the command as can be seen from the frustration of ibn abbas at hajj:
Ibn `Abbas (ra) said: "Stones are about to rain down upon you from the sky: I say to you: "Allah's Messenger said..." and you reply: "But Abu Bakr and `Umar said...?"
Ibn `Abbas (ra) repudiated those who, when they were informed that the Prophet had pronounced upon a matter, objected that Abu Bakr As-Siddeeq and `Umar Ibn Al-Khattab (may Allah be pleased with them both) 2 had said something different, thus, in effect, preferring the opinions of these two pious Companions over the Revelation of Allah.
though we know that the closest companions followed the spirit of the teachings more than the others.
there is a continuing debate on spirit vs letter in every country regarding law
http://en.wikipedia.org/wiki/Letter_and_spirit_of_the_law
And Allah knows best.