Let's first be clear about what asymptotic safety means, in the context of quantum gravity. Quantum field theories that naively make no mathematical sense, can be made meaningful via renormalization. They are regarded as predictive if only a finite number of renormalizations (each calibrated with reference to some measured quantity) are necessary, to make all computations finite.
The quantization of general relativity, appears to produce a quantum field theory requiring an infinite number of renormalizations. Asymptotic safety is the idea that only a finite number of renormalizations will be required after all, owing to nontrivial interactions still existing in the ultra high energy limit of the theory.
There is no proof that any version of quantum gravity of phenomenological interest, actually has the property of asymptotic safety. What has been demonstrated is that some severely truncated versions of quantum gravity (in which only simpler interactions involving the gravitational field are considered) have this property.
If one of these theories of quantum gravity remains four-dimensional at even the highest energies, then yes, I think it has to violate the holographic principle. However, it is possible that such a theory in fact implies a different effective dimensionality at the Planck scale, e.g. because space-time crumples, due to a self-interaction of the gravitational field. This in turn could mean that the microstates of a black hole vary with the surface area rather than with the volume, as implied by black hole thermodynamics.
Occasionally asymptotic safety theorists (or theorists of other approaches to quantum gravity) do claim that their theory has a lower effective dimensionality at the Planck scale, opening the way for consistency with the holographic principle. For example, they may claim (based on some approximate calculation) that the crumpled, lower-dimensional geometries make the dominant contribution to the gravitational path integral.
However, they never seem to be very sure about these claims, nor to offer a clear picture of the quantum microstructure of space. At least, I have not seen any such clear picture. So I have to regard the UV behavior of these quantum gravity theories as uncertain. But the crumpling of space at the Planck scale may be the one chance for asymptotic safety to be consistent with the holographic principle.