the fact that the State has historically had strong ties with the Kingdom doesn't mean that individual corporations or extracorporate initiatives are required to care about said ties.
(all of which is a fancy way of saying: "I don't give a rat's arse")
You want to create new direction for lore by pulling a TonyG on it? Fantastic.
While some might not care on a capsuleer level that the Caldari State is one of the largest manufacturers of TCMCs that keep those 'Matari brothers and sisters' forcibly in check and in bondage. I do reckon majority of the Republic will care, and they will care a lot. You can get branded a race traitor for a far less than working with the same people that actively support the subjugation of your people by providing actively efficient technological means to do so.
The reasons for this alliance initiative seem to be very much wishy washy, and it's clear that people are willing to tonyg lore to make it happen because they don't like some articles or loyalist folk that stand with other factions that are their current allies. You want a new pirate class ship? Cool all well and good... Except that's a bad fucking basis for creating an alliance.
Some the republic loyalist folk seem to like to brush over a good deal of backstory of their own faction and their current allied faction. Much as many republic loyalists hate to admit it but there would be no Republic of any shape or form had it not been for the Federation taking the fledgling nation state under their wing. Sure, these two faction don't see always eye to eye, but their relationship for the majority has been a beneficial one, especially for the Republic. Now that Republic is starting to get to it's own to feet finally it would be unwise of them to betray their long time ally for a mere possibility of something with the State. Tribal, non-tribal, that's just incredibly bad politics as currently really only empire entity that can stand toe to toe with the Amarr Empire is the Gallente Federation based purely on the size of their armadas. Caldari seem to be stretched extremely thin in lore just when they were holding Caladri Prime. If they had to fight the two largest empires in the cluster they'd surely crumble. I can only imagine how the Amarr Empire with their slightly irrational Empress would react to the State shacking up with the Republic.
It would be far easier for the State to get turncoat on their allies if it would serve the greater corporate interests to do so. Granted they would have to be huge, huge enough to cover the financial loss and then some that cutting the ties with Khanid Kingdom and Amarr Empire would cost them. Then there's the Minmatar, who are not exactly known for their open armed welcome for people who have actively worked with slavers and supported the slavery of their kin. As much people like to use the 'corps are like tribes' argument, they really should get their head out of their arse, sit down and do a bit of reading. Compare the current capitalist corporate culture to say native american ( or hell why not scandinavian) shamanistic culture and then please tell me again how similar they are.
Don't get me wrong, there's nothing wrong with change - if you can do it without pulling a tonyg, and so far I see nothing but the desire to tonyg and forget and not care about the existing history and prime fiction. I'd be happy to support such of a player endeavor more if it had more initiative and effort in world building and backstory for it than "we don't care and we want a new cross-race ship".
The reason I am saying this also seems that you guys want to build something of an empire legit alliance. This sort of fuck the systems attitude would more work if you'd go down the line of a terrorist/pirate organization with this initiative. Then it would make much more sense. Besides, you don't get cross racial ships without being pirates