First of all, the use of the word “boycott” in this instance is not inaccurate, but it is a little hyperbolic. You can argue that any personal act is political, but your decision to stop paying for Allen’s films is not a meaningful commercial penalty relative to his stature in the culture. Allen’s contemporary career isn’t dependent on box-office success. At this point, what’s really at stake is his reputation and his cinematic legacy. The bigger question is how you will think about Allen and his work, going forward. How does one separate morality from artistic production? The meaning and significance of that separation is an old question that will be debated forever, and I could never resolve it. As such, I’m just going to address the specific question you asked and its interrelated opposite: Why is it O.K. to stop watching Allen’s films without proof of illegality? And why it is O.K. to keep watching his films if you have doubts about his moral character?
The first answer is straightforward: You don’t need any justification for not watching someone’s films. This isn’t jury duty. It’s an entirely optional entertainment activity. You can elect to ignore a given film for whatever reason you choose; there’s no ethical obligation to have your decision validated by an outside source. You don’t even need to provide a clear justification to yourself: If consuming someone’s work simply makes you feel weird in an unconstructive way, that is enough.