Polarize: To cause a group to be divided into extremes.
This may not fully capture the context you are searching for (specifically regarding freedom of speech causing a directly undesired outcome), but I believe this describes the result of the phenomenon.
As this answer describes:
Polarized opinions does not necessarily imply two opposite opinions, it implies two different opinions.
and while that may seem contrary to my point, it goes on to also say:
Yes, they do tend to be mutually exclusive but they need not be opposite as such.
Example usage (from the linked answer [emphasis mine]):
Our society is polarized with respect to abortion
Further, in a more scientific context,
Group Polarization (Wikipedia): may describe the actual phenomenon you are describing (not just the outcome). In social psychology, group polarization refers to the tendency for a group to make decisions that are more extreme than the initial inclination of its members.