People seem to claim this one way or another somewhat frequently in Imgflip politics sections.
Free speech is legally irrelevant to Imgflip and other private companies. The US first amendment applies to freedom of speech within the nation - not freedom to post your speech on other people's property. Similar concept to claiming one has a right to post signs in someone else's yard.
We try to support open debate insofar as it doesn't violate our terms of service:
imgflip.com/terms