Recent experiments showed that hydrogenation of U₂Ni₂Sn leads to a dramatic change of the magnetic anisotropy (MA) from strongly uniaxial type to easy-plane type with easy axis and easy plane orthogonal to each other. We applied first-principles calculations aiming to understand the microscopic origin of the drastic MA change and distinguish between discontinuous and continuous scenarios of the transformation. The calculations combined with symmetry analysis revealed that the hydrogenation leads to the instability of both uniaxial and easy-plane states caused by the reduced symmetry of the atomic lattice. The obtained noncollinear noncoplanar magnetic states have the features of both apparently competing magnetic structures, which indicates the validity of the continuous scenario of the transformation. An insight into the active interatomic interactions shows that Dzyaloshinskii-Moriya interaction contributes to magnetic transformations and must be taken into account on the same footing as MA.