Does the holographic principle contradict eternal inflation? As it is for example explained here, Andrei Linde's chaotic inflation is among the potential winners or survivors of the spring cleaning induced by the potential detection of primoridal gravitational waves. As this type of inflation is eternal, the new data might also lend some updraft to the multiverse business etc ...

But I always thought that because of the holographic principle, which means when applied to the exponentially expanding universe that stuff moving away can be thought of as being attracted to the cosmic horizon which takes to role of a black hole horizon, it does not make sense to talk about regions or any other universes beyond the cosmic horizon anyway.

So, does the holographic principle contradict eternal inflation as it arises for example from Linde's chaotic inflation? What does the detaction of primordial gravitational waves then mean when taking the holographic principle into account?
There is no obvious implication to re-assess the large-scale topology of the universe.
You can still stereographically project infinity to a point on a sphere, if you need.
Implications to the holographic principle aren't immediate, at least.

When talking about objects beyond the cosmic horizon, it's a difference, whether we talk about observation or mathematical models. When talking about mathemetical models of the universe, it makes sense to talk about space and objects beyond the cosmic horizon, because we can get a higher symmetry of the theory. We can use mathematically simple structures like de Sitter spaces as simplified models of the universe, with no need to add an observer to the structure.

For an evidence-based science it's of course an extrapolation far beyond immediate observation, hence questionable. But there is also no evidence-based argument to assume, that the universe looks fundamentally different from a distant observer with a different cosmic horizon overlapping with our cosmic horizon, but reaching beyond.