No one is advocating for prohibiting people from peacefully expressing their genuinely-held political beliefs in ways that do not infringe on the rights of others in public (unless you want to count the multitudes of minority voters who are regularly removed from voting rolls by GOP lawmakers or subjected to onerous identification requirements and other intimidation tactics...). If a person's "genuinely-held political beliefs" involve racism, sexism, homophobia, etc., and if said person "genuinely believes" that the appropriate way to exert their opinion upon society is to discriminate against the people they hate or even inflict violence upon them, then they are crossing a line established by our societal norms and threatening the stability of society itself.
If a person's genuinely held political beliefs lead them to enact discrimination or violence upon others then they have placed themselves outside of society and are by definition not valid input sources for determining societal norms and laws.