Going round to the terrace, I found three mahogany-coloured Indians, in white linen frocks and trousers looking up at the house. (18.104.22.168)
Betteredge describes the three Indian men as "mahogany-coloured." Mahogany is a dark-colored hardwood that grows in tropical areas – primarily in Central and South America, although some trees from the South Pacific are also called mahoganies. No, this isn't just a random fun fact about trees: it shows that Betteredge's description goes beyond a (racist) reference to the skin color of the three Indian men. He also objectifies them by associating them with a kind of wood that was expensive and exotic – and obtained only by trade with British colonies – during the nineteenth century. He's associating them with exotic luxury commodities.
Now I am not a sour old man. I am generally […] the last person in the world to distrust another person because he happens to be a few shades darker than myself. But the best of us have our weaknesses—and my weakness, when I know a family plate-basket to be out on a pantry table, is to be instantly reminded of that basket by the sight of a strolling stranger whose manners are superior to my own. (22.214.171.124)
Generally, when a person starts to say, "Now I'm not racist, BUT," the alarm bells should start going off. But Betteredge claims, at least, that he feels suspicious, not because of the skin color of the three Indians, but because a) they're "strangers," and he doesn't like things that are strange or new, and because b) their "manners are superior" to his, which suggests that they are of a higher social class than they appear to be. All in all, Betteredge doesn't know what to make of them.
Here was our quiet English house suddenly invaded by a devilish Indian Diamond. (126.96.36.199)
This seems like a strange statement. After all, the Moonstone is just a rock. Betteredge is personifying it when he says that it is "invad[ing]" the house. And he doesn't just refer to it as "the Moonstone"; he calls it "a devilish Indian Diamond." By emphasizing the nationality of the gem, and the nationality of the English house, Betteredge is suggesting that there's more going on here than simply the presence of a troublesome piece of jewelry in his home. The "English house" could be read as a metonymic symbol for all of England, and the "Indian Diamond" is often interpreted as a symbol for India. So for him to say that the diamond is "invad[ing]" the house could perhaps represent the anxiety of many British citizens that the people they were colonizing and oppressing in other countries might actually come back to England and invade them.
'I don't want to force my opinion on you,' Mr Franklin went on. 'The idea of certain chosen servants of an old Hindoo superstition devoting themselves, through all difficulties and dangers, to watching the opportunity of recovering their sacred gem, appears to me to be perfectly consistent with everything that we know of the patience of Oriental races, and the influence of Oriental religions.' (188.8.131.52)
Franklin says that he doesn't "want to force my opinion on" Betteredge, but then he goes on to give a very opinionated and self-confident set of stereotypes about all "Oriental races." He sounds almost like an anthropologist, as though the Indians were an object of scientific study.
In plain English I stared hard, and said nothing. (184.108.40.206)
Betteredge doesn't speak any foreign languages, and hasn't studied foreign cultures like Franklin Blake has, so he keeps his mouth shut – but does it "in plain English."
At the age when we are all of us most apt to take our colouring, in the form of a reflection from the colouring of other people, he had been sent abroad, and had been passed on from one nation to another, before there was time for any one colouring more than another to settle itself on him firmly. (220.127.116.11)
Gabriel Betteredge is obviously using a figure of speech when he says that Franklin Blake was sent to be educated in foreign countries at an "age when we are all of us most apt to take our colouring." What he means is that Franklin was sent abroad at an impressionable age. But he keeps using that word, "colouring," to describe the foreign influence Franklin was given by being educated in other countries. It's possible that he might want to suggest that all of this foreign influence, or "colouring," has somehow made Franklin less English.
As a consequence of this, he had come back with so many different sides to his character, all more or less jarring with each other, that he seemed to pass his life in a state of perpetual contradiction with himself. (18.104.22.168)
Betteredge thinks that Franklin Blake's foreign education gave him some comical form of multiple personality disorder: Franklin has a French side, and a German side, and an Italian side, and, deep down, an English foundation.
The other guest, who sat on my young lady's right hand, was an eminent public character—being no other than the celebrated Indian traveler, Mr Murthwaite, who, at risk of his life, had penetrated in disguise where no European had ever set foot before. (22.214.171.124)
Mr. Murthwaite was a relative stranger to the family before they invited him to Rachel's birthday party. But he's a famous guy, so they invited him to join them. Murthwaite made himself famous by "penetrate[ing] in disguise" into areas of India that no other white people had ever visited. Apparently Murthwaite, a white Englishman, is capable of passing himself off as a native Indian, and this ability to act like a chameleon in India has made him famous back in England.
It left him unsettled, with a legacy of idle time on his hands, and in so doing, it let out all the foreign sides of his character, one on the top of another, like rats out of a bag. (126.96.36.199)
Betteredge thinks that Franklin Blake's "foreign sides" are more likely to appear when Franklin has nothing to do. When he's busy, he acts very "English" and business-like. According to Betteredge, "idle time" is associated with foreignness.
I found him (for example) in the library, sitting under the map of Modern Italy, and quite unaware of any other method of meeting his troubles, except the method of talking about them. (188.8.131.52)
Betteredge's stereotype of Italians is that they only talk about their problems, rather than act. So when Franklin's "Italian side" comes out, he just wants to talk about his "troubles," instead of doing anything about them.