What’s the difference of ‘Truth with capital T” from truth with small t?

This is a good question. Yes, there is a difference between truth and Truth, between nature and Nature, between fighting for a cause and fighting for the Cause. The proper nouns are definite, a unique instance of that thing admitting no others. It personifies it.

See also the song "Ya Got Trouble" from The Music Man:

Trouble. I’m talkin’ ’bout Trouble with a capital T and that rhymes with P and that stands for pool.

By using a capital, it seems more important. It may become an archetype. Or it may be the only one they know. Certainly I as a child did this to special places. It wasn’t just the hill, but the Hill; not just the lake but the Lake; not just the hollow, but the Hollow. There was just one of them for me, and so each of those became for me a proper noun.

Fairy stories often contain such things: the Witch, the Shoemaker, the Woodsman, the Prince, the Castle. This question about J.R.R. Tolkien’s use of capitals from the Fantasy & Science Fiction SE site touches about this. This happens much more in the more fairlytale-like The Hobbit than in the The Lord of the Rings proper, and it far rarer in The Silmarillion or his other serious works where he was more apt to give things like the Sorcerer’s Isle a name in his own invented languages.

Tom Shippey has commented on this practice as being especially noticeable in The Hobbit. It imbues the tale with an easily understood simplicity of language while giving weight to the places named: the Water, the Hill, the Last Homely House, the Mountains, the Wild, the Door, the Lonely Mountain, Lake-town and its Mountain, the King of the Dwarves, the Necromancer. And many, many more.

Used in this way, careful capitalization can create a narrative effect upon the mind of the reader that is desirable in certain contexts. Poets do this when they attribute human qualities to non-human objects or concepts.

We can see this in romantic poet Percy Bysshe Shelley’s poem “The Sensitive Plant”. Here are a few examples from the poem:

A Sensitive Plant in a garden grew,
And the young winds fed it with silver dew,
And it opened its fan-like leaves to the light.
And closed them beneath the kisses of Night.

And the Spring arose on the garden fair,
Like the Spirit of Love felt everywhere;
And each flower and herb on Earth’s dark breast
Rose from the dreams of its wintry rest.

...

For the Sensitive Plant has no bright flower;
Radiance and odour are not its dower;
It loves, even like Love, its deep heart is full,
It desires what it has not, the Beautiful!

Other examples of this can be found in Robert Browning’s poem “Childe Roland to the Dark Tower Came”, whose title is a line from Shakespeare’s King Lear. Browning uses not just the titular Dark Tower, but gives voice to Nature herself.

These stylistic choices can gently lift the narrative from that of the merely mundane to some higher plane wherein abide Plato’s abstractions, things that never fade with time but instead remain forever perfect, for the very reason that they exist only in the mind of Man alone and are therefore all the more real for that, being part of Eternity.

Yes, of course I did that on purpose. Cheap, perhaps. But don’t Man and Eternity seem to become something greater that way?

Politicians sometimes make use of the same technique, or have it attributed to them, as perhaps is being done here in the article you mention. However, their reasons for doing so are seldom so noble as those of poet or philosopher.

"with a capital [initial letter]" is an idiom which refers to an absolute or universal version of the idea.

Obviously, this is political hyperbole.

Little t-ruth is the beliefs, perceptions, ideologies, and rationalizations of the subject and/or subjects. When a scientific institution gives us answers, we get the little truth, because it's filtered through our limited human minds and our social-economic relations. The scientists may simply be incorrect, or the institutions existence may be threatened by accurately disclosing its findings.

Big T-ruth is beyond the perception of the subject, This is what the scientific methodology attempts to identify, and in ideal circumstances the result is a "truth" that is closest as possible to the Truth. Through our inherently limited minds, we are like fish looking out a fishbowl, trying to determine what makes up the bowl.

Denying the existence of this concept is a forceful ideological assertion. Asserting the claim that nothing exists beyond the subject, is the core premise of Fascist ideology. This is what makes Fascism a totalitarian ideology, as it means a subject's will transcends Truth itself.

A material world independent of the subject, which nobody should accept a subject's claim to know it unskeptically, isn't actually being disputed. Nobody disputes this when using something that results from scientific methodology, they wouldn't trust their own life to a consensus opinion, especially when considering the general level of hatred for us simple plebeians.

It is disappointing to see fascist ideology become so firmly established within the humanities. Of course with so much historical revisionism at every step, I may be mistaken assuming it was once anything else. So what exactly is being negated? The idea that they must acknowledge Truth exists beyond their own will, meaning it only exists when they will it to exist. This is post-modernism, or hipster chic fascism, without that crusty old mustache.