Unsupervised node representation learning aims to obtain meaningful node embeddings without relying on node labels. To achieve this, graph convolution, which aggregates information from neighboring nodes, is commonly employed to encode node features and graph topology. However, excessive reliance on graph convolution can be suboptimal-especially in non-homophilic graphs-since it may yield unduly similar embeddings for nodes that differ in their features or topological properties. As a result, adjusting the degree of graph convolution usage has been actively explored in supervised learning settings, whereas such approaches remain underexplored in unsupervised scenarios. To tackle this, we propose FUEL, which adaptively learns the adequate degree of graph convolution usage by aiming to enhance intra-class similarity and inter-class separability in the embedding space. Since classes are unknown, FUEL leverages node features to identify node clusters and treats these clusters as proxies for classes. Through extensive experiments using 15 baseline methods and 14 benchmark datasets, we demonstrate the effectiveness of FUEL in downstream tasks, achieving state-of-the-art performance across graphs with diverse levels of homophily.