I think employers will find it concerning
Employers and recruiters are screening you for scary stuff on your social media -- and they know you know they're looking. Their minds are not on innocent reasons you might do this. When they see two accounts, it looks like concealment: it looks like gaming their screening process. Which they see all the time.
In their world, the simplest explanation is the most likely. Occam's Razor: you're a baddie.
You will need to overcome that bias, and that will depend on their willingness to spend extra time to let you.
The nagging question in their minds will be "why did you do that", when you could've just had accounts on two different social media platforms like everyone else... i.e. a Facebook account for personal and a Linkedin account for professional.
Facebook will be actively hunting you
It's a violation of Facebook TOS to create two accounts. Most of the time these accounts are for sockpuppeting or other system abuses, and Facebook is on the hunt for them. If both of them have your correct identity, that makes you stupid-easy to catch.
Do you really know how to do a browser cookie reset? Clear local storage? Flash storage? It's a constant arms race, as developers try to come up with "supercookies" you can't easily clear. How about IPv6? I'm good at this stuff and I continue to be astounded when I see a highly targeted ad after I was sure I reset everything. Forget about apps - on most phones, Facebook app functionality is too deeply woven into the phone's OS to be able to reset.
Most of the time, account bans are highly arbitrary, because the abuse team is regularly deploying various detection methods, and they just happen to catch you. The account will suddenly just be gone, with no advance notice and no reason why. This can be devastating if you lose a Page or other feature because you are the only admin.
Macs support multiple users (PCs too I hear) and thats probably as good as you'll get for defeating cookies, supercookies etc. But still, same IP address, same first and last name, same birthday, etc...
It confuses your friends
They will search for you and get two hits. With luck, they'll try to befriend both of you. This will be even worse if you falsify some info on one account. They will be confused when you ask them to "please friend my personal|professional account instead" (you're doing the weird thing so you need to do the legwork). Keep in mind, most people let Facebook scrape/surveil their email and contacts, so they'll connect to you via the email they have.
You are probably better off being outbound and friending them first, or answering their friend request with your own friend request from the correct account.
It will confuse you
And you will get confused yourself. You will find yourself on the wrong account all the time. Like I say, switching without being detected is super tricky. You may be better off using one Facebook account always on one device, and another always on another device. Or a different user login on your PC.
Officially Not On Facebook
I've seen it work when the person is Officially Not On Facebook, but has a secret account for utility reasons (e.g. perhaps he runs Facebook ads). He uses a sensible pseudonym and he only tells people who need to know. They understand that his presence is only for utility, not for being social - so they don't engage him socially. It's still a TOS violation, but given their low usage they are unlikely to be caught.