I was a catechist and religious teacher for some time after I left the Watchtower, and I taught Biblical Greek in some of my relgious classes.
This is how you translate the verse, and this is what the verse means:
ἐν τούτῳ γνώσονται πάντες ὅτι ἐμοὶ μαθηταί ἐστε, ἐὰν ἀγάπην ἔχητε ἐν ἀλλήλοις.
With this will know all my disciples you are--if love you have with one another.--My own rough interlinear rendering.
Or as rendered in the ESV-Catholic Edition:
"By this all people will know that you are my disciples, if you have love for one another."--John 13:35.
The idea here is that Jesus wanted his disciples to be self-sacrificing, not merely in serving the public to make disciples, but ongoing once a person was a disciple and part of the group--to the point of dying for one another if the need be. And so this has been the case throughout history from time to time, whether it has been literal or not.
As early as the days of the Church Fathers, Tertullian of Catharge wrote of how people commented about the Church:
“It is mainly the deeds of a love so noble that lead many to put a brand upon us. See how they love one another, they say, for they themselves are animated by mutual hatred; how they are ready even to die for one another, they say, for they themselves will sooner put to death (The Apology, ch. 39).”
The list of matyrs for the faith continues down to our era, many dying for the sake of others. There were grissly deaths of Catholics and Protestants in Asia in modern times, people who died at the hands of persecuting goverments at times in public demonstrations/executions after missionaries were sent away and all was left were these common, native people, many refusing to give up names of others who were practicing the faith. Some of these are now even canonized saints in the Catholic and Anglican faiths.
The JW interpretation has been one limited to how they themselves do good deeds to just members who stay faithful to their own religion. Once in a while someone might lose their lives due to persecution but it is rare. The number of canonized matyrs in Catholicism is over 14,000--that is just those canonized as saints. (See the Martyrologium Romanum Editio Typica Altera - 2004, which is the latest edition.) Many Christians die for their faith every year, out numbering the total of Jehovah's Witnesses who suffer matyrdom.
But the text also has reference to service to people in a way that Jehovah's Witnesses refuse to do, namely to love others as if they were members of their own religion even if they were not. This is how most Christians interpret the text.
They take the text and often see it as a parallel to Matthew 25:31-46 where Jesus talks about seeing and serving him in the hungry, the thirsty, the stranger, the naked, sick, imprisoned, etc. If one can see Jesus in the least of these and serve him in them, then they truly "love one another."
But when people fail to do things like serve Jesus in the least, another text is used in this link:
If anyone says, “I love God,” and hates his brother, he is a liar; for he who does not love his brother whom he has seen cannot love God whom he has not seen.--1 John 4:20.--ESV-CE.
Thus the difference in the way the text is often used by Christians in the mainstream compared to how it has been used by Jehovah's Witnesses. It is used to serve the public by Christianity, whereas it is used to be self-serving in the Watchtower.
