The coalition is built on the common ground of 'smaller govt, strong on defense, etc'.
Yes and nearly all Soc-cons desire that as well. With Rudy it's one sided. The soc-cons get none of their important issues addressed. To make a coalition work, both sides need to give. Giuliani isn't a coalition candidate. Since there are others who could make everyone happy, supporting Rudy can only be taken as an act against the coalition.
The 'important issues' the coalition was built on were the political issues of smaller govt, more local control, strong on defense. Rudy is solid on those issues.
The problem is that the Socials now insist on injecting social issues into coalition. They're changing the contract.