Political polarization has attracted increasing attention in recent years, driven by the rise of social media and the global emergence of far-right populist movements. This study investigates the dynamics of structural polarization during electoral campaigns in multi-party systems, with a particular focus on the presence of far-right actors and their influence on polarization patterns and hate speech. Using retweet networks as a measure of structural polarization, we analyze two case studies in Spain: the 2022 Andalusia regional elections, where the far-right party Vox was a significant contender, and the 2019 Barcelona city council elections, where the party had no representation. Our results reveal that the presence of a far-right party intensifies polarization, leading to the formation of two distinct ideological blocks aligned along left-right ideological axes, as observed in Andalusia. In contrast, the Catalan independence movement in Barcelona diluted the alignment of voters, resulting in a more complex, multi-axis polarization landscape. We also explore the relationship between polarization and hate speech, finding an anti-correlation between them in both cases. Our findings underscore the significant role of far-right movements in driving political polarization and the nuanced effects of different political contexts on polarization dynamics.