As in the title: what exactly is the impact of input bias current in Sallen-Key topology, for example the one below:
I read that it can matter significantly, however I did not find anything more on this matter.
Where did you read that it "can matter significantly"? Well - in principle, it can matter, but only in case you have selected a very bad design strategy with very large resistances and very small capacitors. I assume - in spite of the fact that you spoke about "bias" currents only - that your question concerns the finite input impedance of opamps in general, right?
Of course, each real opamp has a finite input impedance and - besides a DC bias current - there will be always a small ac current into the opamp input terminals. With other words: The opamp constitutes a load to the passive network and - thus - influences the desired filter proprties. (And the same applies to the finite output impedance of the opamp).
However, if you follow the general rules for opamp applications - not to use extremely large resistor values resp. small capacitor values - neither the input nor the output impedances of the opamp play a measureable role for the filter properties. In this context, it is important to realize that there are other non-idealities which have much more influence (availabilty of the calculated ideal values, parts tolerances, frequency-dependent gain of theopamp,parasitics at the nodes,...).
If possible, resistor values below app. 100kohms and capacitor values above 20 pF should be used.
The bias current is a DC characteristic and will not affect the AC characteristics.
In your schematic, assuming Vin is low impedance, it will cause an output offset of -Ib*(R1+R2).
There may be some input resistance or capacitance that could have an effect on the cutoff etc., but Ib is modeled as an ideal current source, which has infinite impedance.