In the wiki it is article only about shear modulus and it is written that it's unit is Pascal. At the same time in all researches about Red Blood Cells shear stresses, authors write "in-plane shear stress" and measure it in N/m. For instance, here - http://web.mit.edu/spectroscopy/research/biomedresearch/B6.html I can't understand why - perhaps it is a difference between in-plane shear modulus and shear modulus. Or it is because membrane is a surface in 3D, not the whole body. Any ideas?
When we talk about shear stress and shear modulus we're normally considering the deformation of a 3D body. However the article you cite is not talking about deformation of a 3D body but instead it's treating the surface of the erythrocyte as a 2D object. That means they use a surface stress which is probably better known as surface tension. This is similar to the way you calculate the deformation of soap films.
Surface tension (and therefore surface stress) is a force per unit length so it's units are N/m, and therefore the surface shear stress has the same units of N/m.