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The speed of light does depend on the motion of the emitter, as posited by Newton's theory. Banesh Hoffmann, Einstein's collaborator, admits that, originally ("without recourse to contracting lengths, local time, or Lorentz transformations"), the Michelson-Morley experiment was compatible with Newton's variable speed of light (c'=c±v) and incompatible with the constant speed of light (c'=c):

"Moreover, if light consists of particles, as Einstein had suggested in his paper submitted just thirteen weeks before this one, the second principle seems absurd: A stone thrown from a speeding train can do far more damage than one thrown from a train at rest; the speed of the particle is not independent of the motion of the object emitting it. And if we take light to consist of particles and assume that these particles obey Newton's laws, they will conform to Newtonian relativity and thus automatically account for the null result of the Michelson-Morley experiment without recourse to contracting lengths, local time, or Lorentz transformations. Yet, as we have seen, Einstein resisted the temptation to account for the null result in terms of particles of light and simple, familiar Newtonian ideas, and introduced as his second postulate something that was more or less obvious when thought of in terms of waves in an ether." Banesh Hoffmann, Relativity and Its Roots, p.92 https://www.amazon.com/Relativity-Its-Roots-Banesh-Hoffmann/dp/0486406768