Note: the concept of "passing " is complex, as I explain in the glossary entry associated with that link. In this post, I will specifically be concerned with trans people passing as cisgender post-transition, as that was the question that was posed to me.
I'm going to start by addressing the more general issue of passing (or not passing) post-transition, before considering the matter of employment/employability.
A lot of times people think of "passing" as an all or none thing, especially going into transition. But in reality, it is more of a spectrum, and in many cases it is contextual (i.e., depending on circumstances and/or the people perceiving you). I've known people who thought that they'd never pass (e.g., because of their size) going into transition who found that they did pass to some degree post-transition. And even people who usually pass as cisgender may be read as trans from time to time.
Regardless of the degree to which one passes as cisgender, there is another important factor to consider: whether or not other people are aware of your trans status, regardless of "passability." So in my case, most people who are trans-unaware read me as cisgender - this is most certainly a privilege that I experience, and it allows me to avoid transphobia in most everyday situations involving strangers. However, I am very out and visible, especially online. So if I were to apply for a job at this point, I'd pretty much have to resign myself to the fact that my future employer(s) will discover that I'm trans in the process. In fact, the one job that I did get post-transition, my employer knew that I was trans right up front, and they were okay with it (partly because they knew my previous boss and trusted his recommendation). My co-workers did not know I was trans at first, although word eventually got around, especially after one co-worker wrongly presumed that it was okay to share this news with others.
I say all this, not to play down the benefits/privileges of "passing" - they are quite real, and there is a tendency (among cisgender and even some transgender people) to view cisnormative-appearing trans people more favorably even when their trans status is known. What I am saying is that all trans people have to deal with the reality of people knowing or potentially finding out about the fact that they are trans. For me, an important first step was coming to terms with the fact that I am trans, and realizing that it's nothing to be ashamed of - rather, it's the people who are bothered by my transness who are the ones with the problem, not me. I had dreamed about transitioning for most of my life, but I was only able to actually go through with it when I finally reached the point where it was more important to be who I was than to live up to other people's expectations.
If you can reach that point of being comfortable with yourself despite other people's inevitable negative reactions, that will go a long way.
But of course, those negative reactions can impact our lives, particularly when they are expressed by prospective employers and co-workers. I was lucky in that, the two places I worked post-transition: 1) my bosses respected me even though I am trans, 2) none of my co-workers treated me with disrespect upon learning I was trans, and 3) my bosses told me that if any of my co-workers did give me a problem, that I should let them know and they would take care of the problem. I think that this is paramount: I know people who are not especially "passable" who have good work situations because they are respected by their boss and co-workers, and I know extremely "passable" trans people whose workplaces were nightmares because (upon learning of their trans status) they faced constant harassment and discrimination from their boss and/or co-workers.
Once again, I'm not saying "passing" (or not) has no impact. But I think having an employer and co-workers who are respectful of trans people is probably the most relevant factor in having employment opportunities pan out.
While we shouldn't have to adjust our lives or occupations to accommodate other people's transphobia, there are a few steps that trans people sometimes take to reduce the possibility that being trans (or non-"passable") impacts their employability. I will list a few of these strategies here. Note: none of these steps are foolproof, and many are not options for everyone. But with those caveats in mind, here are a few strategies that some trans folks I know have taken:
1) If possible, live/work someplace relatively LGBTQIA+ friendly. If you live in or near a big city, or in a more liberal town, it is more likely that there will be decent-sized LGBTQIA+ communities, and that people outside of those communities will be trans aware/friendly/accepting.
2) Some jurisdictions and/or employers will have non-discrimination policies that protect trans people. This certainly won't guarantee you employment, but it can be helpful in the event that you experience workplace discrimination after being hired.
3) Some occupations or employers tend to be more welcoming of gender diversity than others. As a general rule, the more stereotypically masculine or male-dominated a profession, the more problems trans people are likely to encounter in those workplaces. And professions and employers who consider themselves to be open-minded & pro-diversity tend to be more likely to be accepting. Again, there are exceptions to this, but these are general trends.
4) Jobs that are more "behind the scenes" tend to be more open to hiring trans people than jobs where one is expected to interact with customers all the time. (e.g., even if an employer doesn't consider themselves to be transphobic, they may be concerned about their customers having a transphobic reaction to their employees.)
5) Getting jobs through friends or previous employers/co-workers. Sometimes (albeit not always), people who know you and like/respect you prior to your transition will be more willing to look beyond the fact that you are trans (at least relative to random strangers) when considering hiring you.
6) Getting jobs through the community. For example, transgender & LGBTQIA-themed organizations tend to hire within the community. Or people who already work in trans-friendly workplaces will sometimes let others know if a new position opens up there. Often trans & LGBTQIA+ organizations will sponsor local job fairs - that way, you know in advance that prospective employers are at least open to hiring folks from the community. So if there are any local organizations or support/social groups for trans folks in your area, you might want to check them out and/or become more involved in them.
Again, none of these strategies is a "cure all," but they have been useful for some trans people in certain situations.