mgqa:
This is always a tough call, but you probably should apply for the job and you continue with your MBA applications. It's possible one or neither opportunity comes through, so it's a good idea to hedge. Once you have all viable options on the table, you can decide which path makes most sense.
If you are liking the new job and feel it's a real career accelerator, then you can potentially not get your MBA and turn down your acceptances. If you aren't liking the job, you have an easy out. If you like the job but want a program with a 2021 start, you can always quit after 4-5 months and just not put the company on your resume. Sure there would be a gap, but you wouldn't be viewed as a flight risk to prospective employers. If you like the job and end up going for a 2022 intake, then you can gain some experience that hopefully you can leverage for your internships and full-time recruitment.
I am sure there are more permutations and factors to consider, but for now you need to gather options instead of worrying as much about the hypotheticals.
Good luck,
Admissionado