Need help in selecting a model for a classification problem with binary data
Logistic regression models can certainly be used with dichotomous features. It also provides coefficient estimates for each feature so that relationships between features and the target labels can be tested and interpreted. Predictions made from logistic regression models are probabilities rather than binary decisions which can be helpful if you have targets for Type II Error rates, False Omission rates, etc. which is often the case in clinical data.

Distance-based methods can also be used such as the k-nearest neighbor algorithm. With all binary features, it would make sense to use distance measures designed for dichotomous data, such as the Russell Rao distance metric. These models will make predictions based on the class labels of the k-nearest observations in the feature space.