Final answer:
The Republican platform appealed to Californians by opposing the expansion of slavery, supporting free homesteads in the West, promising a transcontinental railroad, and endorsing immigrant political rights to cater to the state's economic interests and diverse population.
Step-by-step explanation:
To appeal for support from Californians, the Republican platform recognized the specific needs and interests of Western states, promoting policies that would directly benefit them. They opposed the expansion of slavery, which aligned with California's status as a free state. The platform also called for free homesteads in the West, the establishment of a transcontinental railroad, and a protective tariff, all of which would support the economic development and political interests of Californians. These promises aimed to garner the favor of Westerners who would benefit from the establishment of infrastructure and the maintenance of free soil territories. Additionally, Republicans supported immigrant political rights, countering concerns linked to the party's perceived association with nativist sentiments, which could appeal to California's diverse population of settlers and immigrants.