s-p mixing is only effective up to Z=7, i.e N2 molecule.
the difference of energy between 2s and 2p is relatively small upto N2, and it has been seen that the sigma 2s orbital gets lowered in energy, and the sigma 2px orbital gets more energised than usual. This is because of similar symmetry of sigma 2s and sigma 2px orbitals, and hence, repulsion between the two. Now, the sigma 2px gets more energised than the pi 2py and pi 2pz also. Therefore the pi orbitals end up filling first, in case of sp mixing.
When there is no sp mixing, sigma 2px will fill first as usual.
So, If you don’t consider sp mixing,
B2 will be: £1s2, £ *1s2, £2s2, £ *2s2, £2px2
C2: £1s2, £ *1s2, £2s2, £ *2s2, £2px2, pi 2py1, pi 2pz1.
(Notice that: if sp mixing WAS occurring, C2 would have been: pi 2py2, pi 2pz2)
Hence, C2 will be paramagnetic and B2 diamagnetic
P.S £ refers to sigma