Discriminatory in Valinor?

[Legolas]

Elves sailed to the Undying Lands in order to find peace. Their immortality can be seen as something of a burden. In their immortal state, they inevitably become quite old (but without the rapid signs of mortal aging), so they desire to embalm (or preserve) the world around them. Unfortunately the world changes faster than they would like, and they are left feeling out of place. The Undying Lands, being the home of the immortal Ainur (Valar/Maiar), are much more conducive to the elves.

Similarly, Men would be completely out of place in the immortal lands of Aman. Men were intended to remain in Arda (incl. Middle-earth), to populate and rule it.

This was part of the Divine Plan from the beginning, which is actually a major theme of Lord of the Rings: the mortal races were always intended to take over from the immortal Elves. The mortal involvement in the War of the Ring is a 'passing of the torch,' so to speak, as the immortal beings take a backseat. Elves are a limited and fading force throughout the story while the wizards are immortal Maiar disguised and constrained by the bodies of old men, sent to inspire the people - not to fight the battle for them.

Towards the end of Return of the King, Gandalf explains as much. First to Aragorn:

And Gandalf said: 'This is your realm, and the heart of the greater realm that shall be. The Third Age of the world is ended, and the new age is begun; and it is your task to order its beginning and to preserve what may be preserved. For though much has been saved, much must now pass away; and the power of the Three Rings also is ended. And all the lands that you see, and those that lie abou them, shall be dwellings of Men. For the time comes of the Dominion of Men, and the Elder Kindred shall fade or depart.'

'I know it well, dear friend,' said Aragorn; 'but I would still have your counsel.'

'Not for long now,' said Gandalf. 'The Third Age was my age. I was the Enemy of Sauron; and my work is finished. I shall go soon. The burden must lie now upon you and your kindred.'

Then to the Hobbits:

I am not coming to the Shire. You must settle its affairs yourselves; that is what you have been trained for. Do you not yet understand? My time is over: it is no longer my task to set things to rights, nor to help folk to do so. And as for you, my dear friends, you will need no help. You are grown up now. Grown indeed very high; among the great you are, and I have no longer any fear at all for any of you.

This is also why Gandalf went so far to include hobbits. He had deep affection for their kind, and wanted to see them grow in stature, able to stick up for themselves - and they do at the end of the story.
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Tolkien confirms that Gimli made the trip as he addresses the nature of it in the published Letters of J.R.R. Tolkien. I think he meant the 'hearsay' bit in the book to be taken as trustworthy - for him, it was a matter of how the authors of the Red Book of Westmarch wouldn't have known firsthand.

From Letter #154, Gimli's entry was by virtue of his special relationship with Legolas and Galadriel:

But in this story it is supposed that there may be certain rare exceptions or accommodations (legitimately supposed? there always seem to be exceptions); and so certain 'mortals', who have played some great part in Elvish affairs, may pass with the Elves to Elvenhome. Thus Frodo (by the express gift of Arwen) and Bilbo, and eventually Sam (as adumbrated by Frodo); and as a unique exception Gimli the Dwarf, as friend of Legolas and 'servant' of Galadriel.

I have said nothing about it in this book, but the mythical idea underlying is that for mortals, since their 'kind' cannot be changed for ever, this is strictly only a temporary reward: a healing and redress of suffering. They cannot abide for ever, and though they cannot return to mortal earth, they can and will 'die' of free will, and leave the world.

The whole letter is worth reading; it is one of the better ones in the book!