Solidarity is a crucial concept to understand social relations in societies. In this paper, we explore fine-grained solidarity frames to study solidarity towards women and migrants in German parliamentary debates between 1867 and 2022. Using 2,864 manually annotated text snippets (with a cost exceeding 18k Euro), we evaluate large language models (LLMs) like Llama 3, GPT-3.5, and GPT-4. We find that GPT-4 outperforms other LLMs, approaching human annotation quality. Using GPT-4, we automatically annotate more than 18k further instances (with a cost of around 500 Euro) across 155 years and find that solidarity with migrants outweighs anti-solidarity but that frequencies and solidarity types shift over time. Most importantly, group-based notions of (anti-)solidarity fade in favor of compassionate solidarity, focusing on the vulnerability of migrant groups, and exchange-based anti-solidarity, focusing on the lack of (economic) contribution. Our study highlights the interplay of historical events, socio-economic needs, and political ideologies in shaping migration discourse and social cohesion. We also show that powerful LLMs, if carefully prompted, can be cost-effective alternatives to human annotation for hard social scientific tasks.