What is meant by "Practice the truth thy brother is same as thou"?

All sentient beings naturally want to be satisfied, yet we typically feel dissatisfaction in our lives. (It is explained in the Four Noble Truths).

Despite our different backgrounds and conditions, we all are equally sentient beings, our minds work by similar principles: we meet problems, we want to solve them.

The root problem comes from illusory oppositions. For example, we divide situations into "me" - "them". Trying to solve problems, we try to make a solution "good for me".

That view - "good for me" - creates attachments. Losing what is "good for me", we feel not just small pain, but suffering, exaggerated by our clinging to "good for me".

And when something hinders our "good for me", we start to hate it.

Thus the oppositions in our view lead to ignorance, attachment and hatred. Also they lead to pridefulness, envy and laziness. And all the other vexations and delusions.

Therefore, in order to liberate from vexations-delusions, we should drop illusory divisions. We should drop our dependence on the view "what's good for me", and instead discover the natural way, beyond oppositions.

That absence of oppositions between all beings is called karuna (compassion), and it is another side of prajna (wisdom). With prajna-karuna we don't separate anyone; we act naturally, for the benefit of all. Without mental blinkers, we are free from ignorance, unhealthy attachment, hatred and so on.

For training in that, it's useful to practice the truth that our oppositions are illusory, deluding and enslaving.

I couldn't find evidence that the Buddha said that.

I wanted to find a more accurate/modern translation than the one you're using. The Sutta known as DN 5 - To Kūṭadanta is the only one I found that mentions Kutdanta ... and it (like the one you referenced) also starts by mentioning "sacrifice" ... but the one you referenced talks about Nibanna and Anatta whereas DN 5 is longer but talks about other things.

The text you quoted is from The Gospel of Buddha:

The Gospel of Buddha was an 1894 book by Paul Carus. It was modeled on the New Testament and told the story of Buddha through parables. ... The work was assembled from existing English translations of Buddhists texts, with significant amendments and reworkings.

Maybe it's good (or was good) as an introduction or overview Buddhism.

It may be reading too much into it, however, to assume that it's Buddhavacana, and to ask questions like, "What did the Buddha mean when he said this sentence?" I think you should treat it as Paul Carus' interpretation (not exactly translation).

For a perhaps more-accurate introduction or translation, people on this site have recommended other books such as In the Buddha's Words: An Anthology of Discourses from the Pali Canon.

I could point to other Buddhist sayings which are like but yet unlike the one you quoted. I agree with Simon's answer, that this phrase you quoted seems inspired by the Christian New Testament.

He is simply affirming as a truth/truism that your brother is the same as you. It's reminiscent of Jesus' "love your neighbour as yourself" -- possibly because of the (originally) Christian background of the writer Paul Carus (who wrote the 1894 The Gospel of Buddha which you're quoting).

The closest message of the Buddha that I can find to this, is Udana 5.1:

When the king, descending from the palace, went to the Blessed One and, on arrival, having bowed down to him, sat to one side. As he was sitting there, he said to the Blessed One, "Just now, when I had gone with Queen Mallikā to the upper palace, I said to her, 'Mallikā, is there anyone dearer to you than yourself?'

"When this was said, she said to me, 'No, great king. There is no one dearer to me than myself. And what about you, great king? Is there anyone dearer to you than yourself?'

"When this was said, I said to her, 'No, Mallikā. There is no one dearer to me than myself.'"

Then, on realizing the significance of that, the Blessed One on that occasion exclaimed:

Searching all directions with your awareness, you find no one dearer than yourself. In the same way, others are thickly dear to themselves. So you shouldn't hurt others if you love yourself.