That Kipling poem is clearly written in the persona of a British soldier, so it is debatable whether the poem itself is racist. It undoubtedly contains racist slurs and assumptions. There's clearly some distance between the first-person I of the poem and Kipling himself. For me the distance isn't big enough. The fact that the overall tone is comic (albeit sourly comic) doesn't help either.

Should you sing it today? The question is rather academic: nobody under 70 would want to. To sing it you'd have to be someone who feels comfortable voicing racist language to comic effect (the idea of which repulses me); you'd also have to comfortable singing a song with a very patronising ventroliquism of a working-class soldier - that in itself would be quite cringe-inducing.

It's not even a very good poem - there are far better Kipling poems you could sing.