Are there any philosophies still claiming the existence of Absolute entities? By Absolute, I mean permanent and independent of cause and effect, such as Plato's One or Forms in general.
Yes. According to the philpapers survey it's quite a lot actually, so around at least 39% lean towards platonism (or existence of abstract objects/properties) and 20% believe in it. So it's fair to say that the position is at least popular with anglophone analytic philosophers.
Like the other comment points out, non-natural moral realists are an example. Another would be belief in abstract mathematical facts (opposed to nominalism).
In contemporary philosophy, Slavoj Zizek operates with the notion of Absolute, though he talks about the "Fragile Absolute". For Zizek, the Platonic Idea as a universal self-manifesting truth has a fragile status, it manifests itself as a temporary event that restuctures the symbolic reality. See his book, Event, he has a chapter on Plato where he develops this theory in detail.