The evidence is sparse, but what little there is suggests that Chiang got along well with Franco, and not with the Republicans. Articles like this one suggest that Franco felt warmly toward Chiang. Franco was not a notably tolerant man, and it is unlikely that he would felt this way if Chiang had supported his enemies in the 1930s. Whether or not China and Spain had diplomatic relations before Franco (probably not), it's quite clear that Chiang had diplomatic relations with Franco (after World War II), and where his sympathies lay.

I agree with your theory number 2. Chiang and Franco were both "Generallsimos." They were both narrow-minded army men who believed in a top-down "command and control" approach to governing. They were both nationalistic, traditional minded men who were fundamentally anti-Democratic and especially anti-Communist. Basically, they were very much kindred spirits.

Chiang was barely anti-Japanese.He started his career as an officer in the Japanese army. Later, he was famous for saying, "the Japanese are a disease of the skin. The Communists are a disease of the heart." Until the Xi'an incident of 1936, Chiang was more interested in fighting Communists than fighting Japan. Basically, the Japanese bungled big time to alienate a "fellow traveler" like Chiang. Their later support of left-wing Wang Jing Wei is best explained as "the enemy of my enemy is my friend."

If Chiang and Franco found themselves with opposite "sympathies" in World War, it would have been accidental, and arisen from the fact that Chiang was forced into an alliance with the U.S. Britain, the Soviet Union, (all of whom Chiang distrusted as a "kidnapper, hooligan, and bully") because of Japanese aggression.

Backstage

I think you place far too much emphasis on ideology. The right/left dichotomy is fairly euro-centric.

The differences between Nationalists/Chiang vs Communists/Mao were quite unlike the differences between Nazis/Hitler and Communists/Thälmann. E.g., I seem to recall that Mao and Chiang cooperated against the Soviet invasion of Xinjiang. Can you imagine Thälmann cooperating with Hitler against Stalin? Or maybe Henlein cooperating with Beneš against Hitler? (no reference, sorry).

Chinese were united is their resentment of the humiliations they suffered throughout the 19th century at the hands of Europeans and wanted to speedily modernize their country economically (and thus militarily) so that it would take the place on the world scene commensurate with its self-assessment.

IOW, the difference between Mao and Chiang was tactical (how to Make China Great Again) while the difference between Right and Left in the European eyes is strategic (what are the proper priorities a society ought to have).

The implacability of the conflict between Mao and Chiang is more circumstantial (ethnic differences compounded by the conflict with Japan, note that the "one ethnic China" is another euro-centric mirage, in fact, China has many dialects) than principled (ideological disagreements).

Answer

The above sets the stage to the answer: since Spain was remote, relatively backward and poor and thus could not contribute much to the fight of Chiang against Japan (and warlords, including Mao), Chiang's attitude was supremely indifferent. He would go through whatever motions were expedient (e.g., since he was supported by the USSR, he would express indignation at whatever Franco did and support of whatever the Communists did, but nothing else). There were about 100 Chinese in the International Brigades, organized by CCP, and I am sure neither Chiang not Franco cared much.

Spain had its own indifference - since they could not affect the Chinese war and could not hope for any help from them, the relationships were probably tenuous at best. They had a skeleton crew in Shanghai International Settlement of course, but not much more.

Further

It's hard to prove a negative (in this case, "nothing interesting existed between Spain and China in the 1930-ies") outside of Math.

You might want to look at books by Paul Preston about Spain (e.g., Revolution and War in Spain, 1931-1939).

On the other hand, China at War: An Encyclopedia by Xiaobing Li does not mention Spain or Spanish in the context of the Civil War at all.