In the movie, the more liberal (and predominantly Catholic ergo 'sinful') mobsters essentially go to war against the Tampa area KKK, due to their association with Cubans and other minorities, as well as being largely Irish & Italian, versus the WASP Klasmen. Is there any historical precedent for this, or was this detail more included to make the audience root more for the mob?
Not just in the US South, but in every state in the union, the KKK was beginning it's second wave, and first membership bubble as a social organization dedicated to fighting "crime" against white traditionalist society. Whereas current estimates of the membership in the Klan across the more than 40 chapters scattered across america is considered to be around 5,000-8,000, the 1920's Klan was roughly 4 million strong, the same size as the current population of the entire state of Oregon.
With that amount of membership, and the countless "shadow memberships" of people sympathetic to the message of the Klan, they were able to forward social agendas that included in the 1920's, support of Prohibition, which oddly was an overlapping agreement point between traditionalists in the Klan and progressive reformers.
With the support of prohibition, there also came the issue of disillusionment with how it was enforced. Many federal and local agencies were very easily persuaded to take a blind eye to bootlegging, moonshining, and gang activity within their areas. So the Klan felt it had to organize itself to fight against gangs and distilleries. Take for example this quote from the EXTENSIVE course notes available here
Just as many disgruntled with the inability of law enforcement officials to make Prohibition work turned to the Klan with its promise to make local communities dry, many women flocked to the Women of the Klu Klux klan as a way of exercising the sort of moral influence on public life promised by the vote. The Women of the KKK, that is, carried into the 1920s a particular strain of suffragist argument. It combined an assertion of woman's equality with an endorsement of woman's traditional roles. It justified women's participation in politics on the grounds that they would raise its moral tone. It appealed to women who had grown up in the Victorian Era or immediately thereafter and had defined themselves in terms of its ideals. However much such women might have bridled at Senator Reed's sarcasm, they would have accepted his verdict that the vote had not ushered in "the prophesied millennium." To such women the Klan made its appeal.
Specific examples of Mob/KKK wars are difficult to raise as much of the activity by both groups in actual violence was done in secret, but there is the story of Charlie Birger which is fascinating as a study of America's shifting morality and the creation of a folk hero.
Anyways, hope this answer suffices