With the ever-growing use of social media to express opinions on the national and international stage, unsupervised methods of stance detection are increasingly important to handle the task without costly annotation of data. The current unsupervised state-of-the-art models are designed for specific network types, either homophilic or heterophilic, and they fail to generalize to both. In this paper, we first analyze the generalization ability of recent baselines to these two very different network types. Then, we conduct extensive experiments with a baseline model based on text embeddings propagated with a graph neural network that generalizes well to heterophilic and homophilic networks. We show that it outperforms, on average, other state-of-the-art methods across the two network types. Additionally, we show that combining textual and network information outperforms using text only, and that the language model size has only a limited impact on the model performance.