Outside of a few specific cases (like the Mayor), all demons in this dimension in modern times are human/demon hybrids. This is reiterated on both Buffy and Angel, and it's pretty easy to find quotes that support this. On the Buffy and Angel wiki:
The Old Ones were the first and most powerful of demons, lived on Earth during the Primordial Age where they were brought from their home dimensions by the Seed of Wonder. However, as time passed, new creatures began to appear on Earth, and the Old Ones either retreated to other dimensions or interbred with humans, thus weakening their powers through the generations. Demons native to Earth were not full demons, but had a percentage of human heritage. Full demons were native to other dimensions.
As a specific quote from the Episode "The Harvest," Giles says
This world is older than any of you know. Contrary to popular mythology, it did not begin as a paradise. For untold eons demons walked the Earth. They made it their home, their... their Hell. But in time they lost their purchase on this reality. The way was made for mortal animals, for, for man. All that remains of the old ones are vestiges, certain magicks, certain creatures.... The books tell the last demon to leave this reality fed off a human, mixed their blood. He was a human form possessed, infected by the demon's soul. He bit another, and another, and so they walk the Earth, feeding... Killing some, mixing their blood with others to make more of their kind. Waiting for the animals to die out, and the old ones to return.
I could keep stacking quotes on here, but this sums up how the deference between pure demons and hybrid demons is laid out in the Buffyverse.
So the question that needs to be answered, since it seems inconsistent with the canonical definition of demons as hybrids, is "Why doesn't the Judge see humanity in Angelus?" I think when you look at what the Judge actually did, and some quotes from the episodes, saying "burn the humanity" out of someone was a little too general. In fact, Angel, before turning, described the legend of the Judge:
It's a legend. Way before my time. Of a demon brought forth to rid the earth of the plague of humanity. To separate the righteous from the wicked... And burn the righteous down. They called him the Judge.
You'll notice that he talks about separating the wicked from the righteous, not separating humanity from demons. Giles also later notes
His touch can literally burn the humanity out of you. A true creature of evil can survive the process. No human ever has.
And we can take a look at demons the Judge incinerated, or wanted to incinerate:
- Spike and Dru, for having affection for each other
- Dalton for having a love of knowledge
The Judge's power only works if somebody has righteous qualities, like love or compassion. This is what is meant by "humanity." When Angelus showed up at the factory after losing his soul, he was devoid of any righteous qualities and back to being a creature of pure evil. Honestly, the Buffy and Angel wiki sums this whole thing up better than I could:
The Judge's main power was to "burn the humanity" out of a person. The "humanity" in question wasn't the presence of a soul in the victim, but the emotional capacity of the Judge's target. While Spike and Drusilla were vulnerable because they shared affection for each other, Angelus wasn't, as he was truly wicked, incapable of love, "clean" before the Judge's eyes.