Adding to the existing great answers (about interdisciplinary research and emerging fields), I'd add perspective by asking, "why are there obstacles at all?". After all, traditionally the degree is awarded as a deliberately non-specific "doctor of philosophy", that happens to be in recognition of advancing the state of knowledge in some specific area, not as a "doctor of chemistry" or "doctor of linguistics" or whatever.
At issue is that in our increasingly specialized academe, hiring is usually done at the departmental level. Therefore, those hiring committees ask, "will this candidate contribute to the reputation, research output, and breadth and depth of expertise in our department?" And also, "will this candidate help us train graduates in our discipline, and/or instruct service courses in our discipline to the broader student body?" And, frankly, "is this candidate like me, so that I can confidently assess their capabilities and fit?"
A senior, respected scholar with sustained research output, that will have necessarily broadened out of the narrow area they started their work in years ago, will present little concern based on what exactly was the topic and awarding department of their Ph.D. years ago. And this will be easily outweighed by the breadth and reputational benefits they presumably bring.
For more junior hiring, it depends on the nature of the position. Where an open position is targeted on an interdisciplinary area, or the search is being run by a specific research team or "Institute" or "Centre", which may well be a part of a conventional department but has some autonomy, there will likely be a lot of openness to candidates from adjacent fields. If it's a hard-fought generic departmental position -- "we've finally got approval to hire another assistant prof in our physics department" -- a newly minted Ph.D.-Chemistry (that did their research in the intersection of physics and chemistry) will face a lot more skepticism: "Will they be able to build and fund a physics lab? Can they teach Physics 101? Which upper year Physics courses will they be qualified to teach?"
The implications is that if you're junior and doing something interdisciplinary, that's great. But I would also consciously build and demonstrate your broader credentials in the standard field you think is most likely to employ you. And you'll have to work harder if you want to prove that in more than one field, or if it's a field that's different from the name of department that will sign off on your "doctor of philosophy" (sic).
Note: Written with a North American perspective. Hiring dynamics can be quite different in e.g. the continental European model.