Generally, I think the answer to this question is yes. There are some elements of this poem that could be argued to be outdated and somewhat anachronistic nowadays. I am thinking specifically of the advice concerning gambling, which was an acceptable leisure activity for gentlemen in Kipling's day but has clearly fallen out of favour in today's world:
If you can make one heap of all your winnings
And risk it on one turn of pitch-and-toss,
And lose, and start again at your beginnings
And never breathe a word about your loss...
Certainly, the specific relevance of these lines is perhaps no longer applicable to a modern audience given the way that gambling is now considered as a vice and an addiction in some cases. However, what is key to realise is that this poem offers us with a series of different ways of showing that you are a "man," and the packaging in which these markers are wrapped can easily be changed. What is important are the kind of qualities that you need to possess. In the above quote for example, the main traits seem to be both daring and a sense of inner-pride and honour that will cause you to "never breathe a word about your loss." Even if the specific example of gambling is a bit outdated, the virtues that this example is used to embody are not. Therefore I would argue that this poem is still just as relevant today as it was in Kipling's day.
and the poem courage by anne sexton
it's the poem if by rudyard kipling