I don't think we can say - not yet anyway - that Mithraism was 'an anti-Caesar cult that re-eneacted his assassination' as part of its 'consciously evil rituals' (much less that this 'something' later becomes what we know as freemasonry and is central to modern-era events like the French revolution). If Mithraism (specifically, this 'late Roman' form of Mithraism) begins only after Caesar's assassination, then Pompey cannot have 'brought it to Rome' because Pompey died before Caesar - which also implies that Caesar's final resting place at the foot of a statue of Pompey is unlikely to mean he was 'pointing to the secretive cult behind his killing'.
(On that issue, Caesar was assassinated in
the Curia Pompey, which is where the Senate was temporarily meeting while the Curia Iulia was being built. Is it unusual then that he would fall below a statue of Pompey in a building that was dedicated to its patron and financier? From
paintings of Caesar's assassination, there seems to have been only one (large) statue on the Senate floor - one of Pompey, naturally.)
The assassins, if some of them were indeed wearing Phrygian caps as they danced out of the Senate on the Ides of March, would thus have been members of something
in existence, not something started afterwards. It's possible, I suppose, that they were members of some semi-secretive club, and that it was
subsequently 're-ordered' to include 'Caesar slaying rituals'. Then, later, narrative about Phrygian caps on some assassins' heads was penned in order to retroactively leave a signature on the assassination. But you can see here that I'm having to make two additional assumptions to make things chronologically consistent.
Separately, given that we know who Caesar's enemies were, and what their ideological beef with Caesar was, I don't see the need for 'exposing a secretive group' that linked those enemies together. It's kind of like today's situation in the US; Trump sees his role as defending the constitutional republic from bankruptcy, war, decay, etc., and his enemies
also see their role as 'defending the constitutional republic'... from Trump! Once you can see the general situation, do you need to establish that the Cheneys, Clintons, Bushes, Nulands, and Kagans are all part of a specific club? Trump's run as a 'populare' effectively 'busted wide open' the existence of this 'secretive cult'!