Is "You’re a better man than I am, Gunga Din!" still considered a compliment in English?

It's a cardinal error to confuse a depiction of bigotry with bigotry itself.

Yes, the narrator of the poem is racist, not only by modern standards but in the opinion of the author of the poem. The juxtaposition of the disdainful attitude of the soldier with his candid admission that the blackfaced heathen slavey whom he beats and abuses is, in fact, the braver, better man gives the poem its power.

You Lazarushian-leather Gunga Din!
Though I’ve belted you and flayed you,
By the livin’ Gawd that made you,
You’re a better man than I am, Gunga Din!

Given that a few, presumably well-read, people here have different recollections of the poem, and different interpretations, you would be unwise to make assumptions as to the effect on your audience. Many people's reaction would be along the lines of “you what?” having never heard the quote and not even recognising it as a quote, never mind a poem or Kipling.

Those of us who studied it in the dim and distant past may remember racism in the context — but not in detail. We may remember (if we’ve read a little on the subject) that Kipling’s views are the subject of much discussion. My understanding is that while racist by today’s standards he was unusually progressive by the standards of his time in at least some aspects of his treatment of the natives.

At best, quoting Kipling will seem old-fashioned (with the possible exception of “If—”) . So I suggest you only use the quote if you don’t mind people thinking you’re a (possibly racist) dinosaur. If I were in the audience, I would give the speaker the benefit of the doubt, but that’s about me, not the quote.

Finally, although the narrator is expressing admiration (even without the racial aspects we can’t ignore) it boils down to “for someone who’s my subordinate, you’re a better man than I am”. After all, the narrator had the right to beat Gunga Din. This may not be the impression you want to give.

My dad (native to Oklahoma) uses it, and I picked up the usage from him. I believe I've heard my mother-in-law (native to Ohio) use it as well.

The way we use it isn't a compliment. Its more an observation that the person in question is undergoing a lot of (potentially hazardous) work for no really good reward. It would be used in a lot of the same contexts as "Have fun storming the castle!" (Princess Bride callback), "Good luck with that", or "Better you than me."

Many thanks for directing my attention to this intriguing and controversial poem from one of the Children of Empire.

"A racist would not have glorified Gunga Din in the way Kipling did," wrote Andrew Roberts in The Telegraph on 13 May 2003

http://www.telegraph.co.uk/comment/personal-view/3591241/At-last-Kipling-is-saved-from-the-ravages-of-political-correctness.html

and having read the full text of Kipling's famous poem, I fully agree with him, Indian that I am and a long time reader of Literature!

It is well known that Kipling had great love for India and for Empire. Lines taken in isolation may paint a nasty picture, but each poem should be read in its entirety, in context, and I am convinced there is nothing inherently racist about 'Gunga Din'.

It is amazing to see that Kipling and Mark Twain have become controversial -- are their opponents even reading their works before donning the armor of righteous indignation to do battle against the ghosts of two great humanists! In fact that is the bigotry of ignorance, absolutely incapable of recognising oblique sarcasm or self-reflexive irony, and it shows that nuance is dead!

HOWEVER, you are asking about the statement 'you are a better man than me, Gunga Din!' -- that line is by itself proof that it is not a racist poem, but earnestly politically-correct non-readers who have mentally 'tagged' Gunga Din (possibly without reading it) as a racist work may be vocally offended, especially those of the left-leaning liberals (not all but some) who are unforgiving of all imperialism except the dictatorship of the proletariat, which alone is historically and ideologically justified.

Moreover, as already pointed out in the earlier comments and answers, the vast majority of people just may not get the reference!