So I solved by changing my Dockerfile to:
FROM docker.elastic.co/beats/filebeat:8.10.0
COPY --chown=filebeat filebeat.yml /usr/share/filebeat/filebeat.yml
RUN chmod go-w /usr/share/filebeat/filebeat.yml
I don't know if this is the best way to do, but it worked.
If this configuration poses any risk, please, let me know.