How "cursed" would a carlist Spain be?

Carlism is a Spanish catholic monarchism moviment as you probably know, supporting a return for tradition and the appointment of the Carlist branch of the house of Bourbon to power in Spain

Carlism never representated most of the spanish population, and on the civil wars they fought they always were strongly outnumbered, until the final one that was the Spanish civil war where the Carlists supported Franco, just to be stabbed on the back with Franco appointing the main branch of the house of Bourbon to succed them, and since the end of the Francoist dictatorship they have drifted towards a more progressive branch of carlism, while also being driven to borderline irrelevancy

Let's say that for some reason they end in power of Spain in 1930s and install their claimant Javier of Bourbon-Parma as the King of Spain, would Spain turn into a fundamentalist catholic state and close itself from the world?
Would a carlist Spain be more or less likely to enter WWII (on either side)?
I wouldn’t expect so at all. They would like Franco be focused upon eliminating the working class communist and anarcho-syndicalist opposition, but I could not see them risking entering the war
The main branch was supported by Liberals and some more "ungodly" factions and, on top of that, the heir was a woman. Utterly terrible for them.
The carlists always confused me. Why did the cadet branch matter so much?

Because under the Bourbons Spain had the Salic Law until 1832, when Ferdinand VII made a will in favour of his daughter.

But it was not at all clear that he had the right to do this. The Salic Law had been adopted under Philip V by a Cortes, not simply by Royal proclamation, and arguably could only be revoked in the same way, so Ferdinand was exceeding his powers. Indeed, iirc, when Ferdinand was critically ill in 1832, his Ministers, on discovering the will, were totally flabbergasted, and decided to keep it under wraps until Carlos was safely on the throne.

However, Ferdinand made an unexpected recovery, and on learning what had happened, appointed new Ministers who were prepared to comply with his wishes, so that on his death the following year, his daughter was duly proclaimed as Isabella II. But Carlos and quite a few others were not prepared to go along, hence the civil wars that followed.
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