Text classification is a central tool in NLP. However, when the target classes are strongly correlated with other textual attributes, text classification models can pick up wrong'' features, leading to bad generalization and biases. In social media analysis, this problem surfaces for demographic user classes such as language, topic, or gender, which influence the generate text to a substantial extent. Adversarial training has been claimed to mitigate this problem, but thorough evaluation is missing. In this paper, we experiment with text classification of the correlated attributes of document topic and author gender, using a novel multilingual parallel corpus of TED talk transcripts. Our findings are: (a) individual classifiers for topic and author gender are indeed biased; (b) debiasing with adversarial training works for topic, but breaks down for author gender; (c) gender debiasing results differ across languages. We interpret the result in terms of feature space overlap, highlighting the role of linguistic surface realization of the target classes.