They obviously belong together. The people in charge of the system as it stands only have short-term, personal interests as their motivation. The states, corporations and financial cartels that control the world are clearly set on maintaining their destructive course. Breaking the existing power structures will greatly improve any possible outcomes of the 21st century.
So given the above, how can we bring the collapse movements and anticapitalist movements closer together?
Currently many of these groups are working at cross-purposes. Most of the climate change and general environmental movements are liberal-left in orientation. They get bogged down in trivial and symbolic activism. Many of them are duped by greenwashed capitalism. The peak oil scene has really fallen apart in the last ten years, despite the likelihood that we're in the last days of cheap petroleum right now. Most of the die-hard figures of this movement are right-of-center, notably the social conservative James Kunstler and the paleo-conservative (but highly insightful) John Michael Greer. Meanwhile many anticapitalists are blind to the hard limits that exist in natural systems. They tend to take as blindly naive views of industrialism as capitalists. If they really took a systems approach to the challenges humanity faces, they would have to change priorities and tactics.