I can't think of any workplace discrimination that could happen against asexuals. If anything, it's the opposite. Gay people have been discriminated against at work because of bigotry. Women have been discriminated against in the workplace because of their marital status and the fear that they might get pregnant and take time off work. From a workplace discrimination point of view, employers would probably prefer it if their employees never hooked up, risked getting STDs that might require their insurance to pay, risked getting pregnant that might require maternity leave, or risked getting married, which might mean bringing your spouse onto their health insurance. Plenty of workplaces would probably love it if all their employees were single and sexless their whole careers.
Asexuality MIGHT bring some social stigma, in the sense that your parents keep pestering you to get a partner/get married/whatever, or because people say you're too ugly to get laid, call you an incel, etc. But that's not really discrimination, it's just rudeness. Incels aren't discriminated against, either. Maybe at work, depending on the culture, people might look askance if you're not dating or talking about sex, and that would probably bug asexuals and incels for different reasons. But nosy people at work =/= discrimination.
I can't think of any other avenue where discrimination against asexuals would even happen. When the cops pull you over, they don't know if you're having sex or not. Shop keepers can't tell, and thus can't deny service based on it. "Couples only" services don't discriminate against asexuals or incels, they just exclude people who aren't currently in a relationship.
I remember reading about Don't Ask, Don't Tell, and one of the arguments against it was that when soldiers are bonding with each other, and straight soldiers are allowed to talk about their girlfriends but gay soldiers aren't allowed to talk about their boyfriends or take part in the conversation, that creates a way that they are othered and excluded, and not "one of the guys." I can SORT of see this extending to asexuality, but only if there's a similar Don't Ask, Don't Tell policy in place. If everyone is talking about their sex life, and you say "I don't have a sex life because I don't want one," that is WAY different than being literally NOT ALLOWED to say anything about it. One is perhaps uncomfortable, but the other is actually discrimination.
I'm willing to accept that asexual people sometimes feel uncomfortable or judged, since we do have a prevailing assumption in our culture that romantic pairings are the key to happiness, and sex is very important to life, etc. But people are uncomfortable for all sorts of reasons, that doesn't mean it's Oppression or Discrimination. I also think "asexuality" is really just people with lower than average sex drives, or for whom sex just isn't as important as it is for other people. Maybe the end result is someone who never pursues sex, but I don't think it's a label that actually helps anyone. It's definitely not in the same realm as LGBT. But whatever, you do you, hypothetical asexuals.