While sample and feature order can have subtle effects on the model fit by an estimator, I think we should have common tests to ensure that reordering or subsampling X in predict or transform or score_samples or predict_proba or decision_function does not change the sample-wise output. That is:

idx = np.random.randint(X.shape[0], size=X.shape[0] // 2)
assert_array_equal(method(X)[idx], method(X[idx]))

Apologies if we already have such tests, but I can't see them (which is also an issue: we don't actually have a clear list of what is asserted by estimator_checks)