With the rapid improvement of machine learning (ML) models, cognitive scientists are increasingly asking about their alignment with how humans think. Here, we ask this question for computer vision models and human sensitivity to geometric and topological (GT) concepts. Under the core knowledge account, these concepts are innate and supported by dedicated neural circuitry. In this work, we investigate an alternative explanation, that GT concepts are learned ``for free'' through everyday interaction with the environment. We do so using computer visions models, which are trained on large image datasets. We build on prior studies to investigate the overall performance and human alignment of three classes of models -- convolutional neural networks (CNNs), transformer-based models, and vision-language models -- on an odd-one-out task testing 43 GT concepts spanning seven classes. Transformer-based models achieve the highest overall accuracy, surpassing that of young children. They also show strong alignment with children's performance, finding the same classes of concepts easy vs. difficult. By contrast, vision-language models underperform their vision-only counterparts and deviate further from human profiles, indicating that naïve multimodality might compromise abstract geometric sensitivity. These findings support the use of computer vision models to evaluate the sufficiency of the learning account for explaining human sensitivity to GT concepts, while also suggesting that integrating linguistic and visual representations might have unpredicted deleterious consequences.