You're comparing satire to light entertainment. The "Colbert Report" was satire (on cable!), and Colbert's current show is a light entertainment talk show (on a network!). They have different forms, different audiences, and incommensurate goals.

As in South Park, satire even today seems to grant a license to the performer that isn't there in light entertainment.

Here's an example: there's a trope that Colbert, Bill Maher, SNL Weekend Update, and many others use that goes like this:

1. Unstated premise: Anti-$foo politician exists.

2. Premise of joke mentions something that is related to deplorable anti-$foo sentiment

3. Punchline is the comedian attributing an anachronistic anti-$foo street joke to said politician

The only person I ever heard complain about this trope was Norm MacDonald wrt anti-gay conservative pundits who had been outed as gay. (Though it's Norm, so I'm not sure if he was just trying to a get a rise out of a guest or really thought there was some bona fide double-standard going on here.) To be fair the comedian is in a way "laundering" the humor from the old street joke, but most people seem to understand the upshot as showing the object of ire as being out of touch/ignorant/etc.

The humor on the "Colbert Report" was similar, but more intense-- Colbert was publicly playing a homophobic/racist/narcissistic ignoramus built in the mold of a Bill O'Reilly. For years.

In the clip you linked, I'm guessing his character was a) reflexively lumping in the word "hispanic" with the topic of illegal immigration, and b) using that connection as a fear-mongering tactic to persuade his audience to be suspicious of hispanics even in the conceptual domain of a fucking calendar.

Colbert of the Colbert Report usually got away with that-- if a viewer from his audience switched to his show in the middle of it and saw him wearing that hacky getup, they'd likely assume it was satire, suspend disbelief, and look for the upshot of the joke.

But even given that, it didn't always work. Colbert did indeed get flak on "Colbert Report" for taking this approach with a recurring bit about Asians. The bit was built on a long-standing satire trope where a comedian/writer pretends to fix a racist logo, slogan, book, or even a slur itself by shifting it from that target group to an Asian ethnicity. The undertone would be that it's somehow less dangerous or problematic, with an implication that the Asian ethnicity in question is less likely to complain or fight back. You can see Sarah Silverman telling such a joke on an old episode of Conan (for which she was called out), so the trope has been around since at least the 90s. Turns out that people tend to look down on satire which tries to call out prejudice by unwittingly relying on other prejudice.

Regardless of whether you agree with the calling out of those particular bits, the following are true:

1. Sarah Silverman was called out for her satire on a light entertainment show in the 90s

2. Colbert was called out for his satire, even on a satire in the 2000s

3. Colbert of today runs a light entertainment show where the satire of #2 is much less prevalent, which likely explains why he doesn't do bits anything like what he did in the "Colbert Report"

In conclusion, on this particular topic: times have not changed.

Thank you for your time.