Well, I'm sure that we all agree that 'Paki' isn't a very nice word, and that coupled with the words 'go home' (or even worse) is very nasty indeed and seriously offensive.
But why such a fuss because a young man uses it as a nick name for a friend?
From time immemorial men and boys have given their friends not particularly complimentary nicknames: 'Piggy', 'Four-eyes', 'Titch', 'Ginger' etc. even the N word if the friend happened to be dark. A lad may not have been overjoyed by the choice of nickname, but to an extent it indicated that he was now an accepted part of the group. My father (82) is still Titch to a few people.
We have only to look at a whole class of surname - two whole classes of surname - to realise that identifying people by their physical appearance or by where they originate dates back at least to the middle ages. If your name is Redhead or Curley, Toogood or Toplass you can be sure that you know how some mediaeval ancestor looked or behaved, while almost any place name indicates that an ancestor was at one time an outsider who came from another town or village while Jewson or Ingalls, Welch or Scott may indicate a family which travelled further than a few villages.
Come to that, and going even further back in time, what is Flavius but the Latin for 'blondie'?
In other words context is everything. I would not revel in being nicknamed, let us say, 'fatty four-eyes' however justified such an epithet may be, and I would be astonished and deeply offended if, for example, Hilary (at work) or Veronica (in the village) chose to address me thus - and you too would be equally astonished if you knew these two ladies. On the other hand if my brother-in-law decided that was this week's nickname for me I wouldn't be particularly surprised or hurt since his idea of a friendly and humorous greeting is to insult the person he is addressing - silly and irritating, but his way.
If a stranger shouted out to me "Move now, fatty four-eyes" and thus saved me from falling scaffolding or a run-away lorry, I would take that as being the swiftest way he could identify the person who needed to shift and certainly not be offended. 'Paki' or even 'N-----', used in the same context would surely be equally lacking in offence.
When it comes to racially based nicknames at what stage does it become offensive? I am proud to be a 'meggie' (native of Cleethorpes) and a 'yellerbelly' (native of Lincolnshire), and presumably people feel the same way about Scouser, Geordie, Brummie etc. 'Yorkie' presumably means no more than a native of York or of Yorkshire and will thus be used with similar pride; however 'Yorkie' (or more especially 'bloody Yorkie') as used by a meggie is a term of abuse referring to a particular type of uncouth day-tripper from south Yorkshire who spends the day getting drunk and throwing up all over our seafront and cliff gardens. (It's all a matter of context.)
At what point in this list of racially based nicknames do we move from simple identification to insult? Scottie? Jock? Taff? Paddy? Mick? Aussie? Yank? Frog? Fritz? Wop? Chink? Paki? They are none of them words I would personally use, but I wouldn't be offended if called Limey, Pom or Roastbif - they are only words - and if one of my nephews or godsons had such a nickname in regular use it would be none of my business to mind on his behalf or to demand and apology for such language. If he didn't like it, it would be up to him to tell his friend he found it offensive or childish.
And if my nephew's or godson's friend happened to be the younger son of the heir to the throne, which is really more offensive to all our sensibilities: the person who privately uses a nickname which might be held to be racist, or the person who records private conversation and releases it to public scrutiny knowing full well the result of such an action?
Boys will be boys, and using mildly derogatory nicknames for each other is and always has been a part of their culture when they get together.
Maybe we should go further and suggest that all such names are grabbed by their communities, dusted off, and worn with pride so that words - only words - which were once seen as an insult become both a badge and an aspiration to reflect all that is best in their culture.