Acceleration can't be universal if by that you mean every existing thing. You must be moving relative to something or the velocity is not measurable. In RE, we simply don't know if the known universe as a whole is accelerating or moving in any way. In FE, at least the most common version, the entire known universe is the surface of the earth, the sky, and maybe a dome.
Are the stars fixed on the dome, or are we moving universally with them? What is universal acceleration in relation to? Perhaps there must be something but we can never see it? Perhaps we only know that because Michelson-Morley we know the earth is flat, and because things fall at 32 ft/sec/sec we know it must be accelerating? That would be taking the falling object as the reference and the rest of the universe as moving. Can we ever have an external reference?
Please advise any error I may have made. Hope to hear some good answers.