Literally, ‘rimé’ means a ‘non-sectarian’ or ‘non-biased’ view. While some people may think this is related to the idea of all systems being equal, it is actually focused on recognising the value and benefit of multiple points-of-view.
One way to understand this is to consider how we use medicine. There are many medicines and each has the capacity to cure specific types of sicknesses. We do not normally mix our medicines. Instead, we recognise the specific needs of each patient and choose the right medicines for helping them overcome their problems.
In the same way, developing a Rimé philosophy means knowing how each system works, what are its defining characteristics, what are its strengths and how can it be used to alleviate dissatisfaction. While we may have a personally favourite view, a favourite practice or a favourite system, there is no contradiction. We can hold a non-sectarian view while recognising that specific practices and teachings are especially suited for our needs.