You can minimise it and yes, even eliminate it through sensible policies, like sanitizing race from the equation and making decisions in a blind manner: having showing itineraries built by people not exposed to the race of the applicants.
Of course, the easiest way is to just revoke the business license of those agents who clearly act on prejudice.
You're proposing exactly what I did: if you don't have the infrastructure to express your prejudice, it doesn't matter.
Whilst such measures would likely help, I think saying that prejudice doesn't (or wouldn't then) matter is going too far and I don't think Jarhyn was saying that. His previous remark that prejudice always matters because opportunity to act on it is a function of time, was on the money, imo.
But the idea that prejudice, a bit like crime perhaps, is inevitable, and that all that can be done about it is to try to stamp it out or regulate it using various procedures and protocols, is an incomplete perspective, imo. Some prejudice may indeed be inevitable, but the particular amount is not, and the associated problems are generally a matter of degree. And furthermore, efforts to regulate it arguably don't get to the core of why it manifests to the degree that it does in the first place, nor do such efforts do much to treat the underlying causes. In some ways, it's enforcement/regulation as a post hoc sticking plaster.
Herein lies the broad moral justification for also, in addition, doing more to acknowledge, address and indeed try to actively rectify some of the underlying and historical issues and the factors which have in part caused the patterns (and degrees) of inequality and unfairness that manifest in any given society in the present, be they economic, cultural, gender-based, racial, or whatever. Much of this could arguably come under the broad umbrella term 'social justice', which has become an unfairly maligned concept in some quarters, imo.
Personally, I don't think it's easy to get towards more or better social justice (a 'fairer society') without doing at least something, sometimes something broad or structural, to remedy (and possibly offer some redress for) the (often historical) causes, something restorative in other words, though I do accept that it is very tricky to work out how to do that effectively and with due consideration towards fairness for
all current members of society, privileged, unprivileged or whatever, and their individual liberties. But I believe the moral case for it is strong, at least in principle, which is why I would advocate for people being more tolerant when it comes to allowing such things to be discussed, proposed and pursued, partly because the vast majority of people stand to benefit in the long run.
I guess those last two paragraphs are very general, and away from the specific OP issue somewhat.