Does SM allow for the right-handed (Majorana) neutrinos? Or right-handed neutrinos are beyond SM?
There is no right handed neutrino in SM.
Antineutrinos are produced in nuclear beta decay together with a beta particle, in which, e.g., a neutron decays into a proton, electron, and antineutrino. All antineutrinos observed thus far possess right-handed helicity (i.e. only one of the two possible spin states has ever been seen), while neutrinos are left-handed. It is possible that their counterparts (right-handed neutrinos and left-handed antineutrinos) simply do not exist. If they do, their properties are substantially different from observable neutrinos and antineutrinos. It is theorized that they are either very heavy (on the order of GUT scale—see Seesaw mechanism), do not participate in weak interaction (so-called sterile neutrinos), or both.
Sterile neutrinos (or inert neutrinos) are hypothetical particles (neutral leptons – neutrinos) that interact only via gravity and do not interact via any of the fundamental interactions of the Standard Model. The term sterile neutrino is used to distinguish them from the known active neutrinos in the Standard Model, which are charged under the weak interaction. This term usually refers to neutrinos with right-handed chirality (see right-handed neutrino), which may be added to the Standard Model. Occasionally it is used in a general sense for any neutral fermion, instead of the more cautiously vague name neutral heavy leptons (NHLs) or heavy neutral leptons (HNLs).
At least without an extension. These kind of extensions (that include the right handed neutrino) do exist. Weinberg operator is usually used.