In my opinion, an Antheist can be compassionate. To love and to be loved is universal, regardless of who you are, rich or poor, fat or thin, young or old, we want to be loved and of course to love. It is also taught in the school which is not a religious place that as a human we should care about others, including animals.
With a religion belief(that is pure, not contaminated), we follow a method or way to help is generating compassiom towards others. For instance, the prayers serve as a positive affirmation for us to generate compassion. Prayers in any form of religion (again a pure and uncontaminated one) always include statement such as to help, to love and to forgive.
An Atheist without any religion belief can have compassion if they grow up in an environment full of love. However, without a religion, it might take them longer to gnerate compassion.
In short, in my opinion, it is possible for anteists to have compassion.