[RPG] Does the damage from unarmed strikes bypass non-magical/silvered/adamantine weapon resistance and immunity

Short answer: Yes.

Long answer: There is some leeway that is up to the DM to decide. Basically, it comes down to whether the magical effect of the weapon is diffused within it or is simply a layer on top. A Paladin's Smite, for example, does not make the weapon magical despite magic surrounding it.

Normally, this is an unnecessary distinction. All of the magic weapons in the DMG are like this by default, but a DM could change it. For example, a Weapon of Warning that was gifted to a PC by a deity could be one that is just an enchanted weapon (and so counts as a magic weapon), or it could simply be an enchantment over the weapon.

As a DM, I would recommend leaking this information out to the players through an encounter with a lesser danger (a lycanthrope that can be easily wrestled or dispatched with spells, or something with only resistance). Since the default of the game is that the magically-imbued weapons they have received are treated as magic weapons, placing the PCs against a foe immune to them with no warning to this change could be seen as antagonistic.

Making the answer as simple as possible: a snippet of Spiritual Weapon description:

Clerics of deities who are associated with a particular weapon (as St. Cuthbert is known for his mace and Thor for his hammer) make this spell's effect resemble that weapon.

It is not a weapon. It is a 2nd level spell whose effect resembles a weapon. The Rakshasa is immune.