Text classification for data with multiple labels per observation
There are different options:


Multi-class classification: each tweet can be labelled with several classes
Majority voting: each tweet is labelled with the class chosen most often
Consider tweets with (too many) different labels as ambiguous and remove them from the dataset
...


Additionally it's usually useful to calculate the inter-annotator agreement, because this indicates how subjective the task is and therefore how accurate one can expect the predictions to be.