Romans were perfectly happy to be associated with headhunting, despite some claims you may occasionally see to the contrary (Richmond in his book on Trajan's Column rejects categorically the possibility of Roman headhunting, for instance). Jean-Louis Voisin has a 1984 article that catalogs many cases. I have severe problems with this article, but it hasn't got the attention it should have (and neither has my unpublished MA thesis - full disclosure - which is largely about how wrong Voisin was about his argument, but he's right to say Roman headhunting was a thing).

There are plenty of stories of individuals taking heads as part of duels, taking heads en-mass, taking heads to prove identity of the dead, all kinds of stuff. Sometimes headhunting stories can get quite nasty, such as the accusation that Opimius offered to pay its weight in gold for the head of C. Gracchus, but they can also be laudable stories, such as C. Gracchus' grandfather Ti. Gracchus, who commanded a slave army during the worst part of Punic 2, and who promised freedom and citizenship to every soldier who could deliver him the head of a Punic soldier. A quaestor, M. Sergius Silus, even put his grandfather in the act of hunting heads during Punic 2 on a coin.

Headhunting was part of both Sulla's and the triumvirs' proscriptions, and not even for IDing the victim necessarily. One story has Nero, when seeing the severed head of Plautus, say he would have spared the guy if he knew how big his nose was - implying he didn't know before. There are stories of Sulla's proscription in which random people were killed in place of those listed, because Sulla or his men couldn't recognize them.

I don't see any reason to think the auxiliaries here were somehow being less than Roman with their participation in headhunting. It WAS a Roman thing and WAS celebrated.

I don't know what that has to do with guilt by association though.

I don't understand what you mean by guilt by association here.

I think I understand your question, which is overly broad. So, to help, you should clear up some terms.

First, you are using a modern sense of barbarism which is different from the ancient meaning. Barbarian literally means someone who did not speak Greek (where the term originated). While that would include most Romans, to a Roman a barbarian was someone who was not Roman or did not follow Roman conventions (like baths, speaking Latin, shaving, etc). In a modern sense, barbarism is acting with disregard to human conventions: prohibition against senseless destruction, against terrorism, etc. The two concepts of barbarism are not the same.

Second, I understand what you are trying to say about differences between auxilaires and regular legionaires. But in this case, it does not matter. What you should focus on is that the severed heads have beards on them and the men holding them do not. Also, the men holding the heads have Roman shields, tunics, helmets, and are paying homage to the emperor. The message here is: 1. Romans (i.e. Trajan) are victorious; 2. bearded barbarians (i.e. Dacians) lost and are humiliated.

The column is propaganda for the folks back home and for the ages. It is Roman column intended for a Roman audience. And while modern audiences may be shocked by soldiers severing the heads of the people they killed; it is not the case for an ancient audience.

Yes, the column is propaganda. It shows the power and might of the Roman army on the move. It takes a lot of logistical will and man power to put legions in enemy territory, subdue it, and begin colonization. And I would not say that Romans are disassociating themselves at all. In fact, they are proudly displaying their ability to defeat non-Romans.