Participation in climate activism is often facilitated by joining groups on digital platforms, for online and in-person participation in the movement. However, despite the easy access to communities digitally, people of colour (POC) are underrepresented in the UK in climate activism. Little research provides insight into why the voices of POC are underrepresented and how to level the playing field for participation in climate activism, which is just as important to POC. To investigate this, we conducted a qualitative semi-structured interview study with POC who are active in the climate movement (N=12). We identified five main themes: (i) gaining membership to the climate activism community, (ii) experiencing challenges in belonging with respect to identity characteristics, (iii) participating in protest through relevant issues and values, (iv) feeling fear due to differences and marginalisation, and (v) developing strategies for control and utilising anonymity. Our findings show how people's racial and other minoritised identity is crucial in influencing their sense of belonging and community and in turn their participation in climate activism and perhaps other opinion-based movements. For movements to be more inclusive, we urge the HCI and CSCW community to rethink designs influenced by structures of power and centre diverse values and issues instead of universal ones to amplify the voices of minoritised identities. Suggestions on how technologies could achieve this are discussed.