Personal beliefs are the foundation of your value system. These concepts and principles which you hold to be true are the fundamental drivers of your behavior.
We are not always able to sustain our beliefs. External factors ranging from environmental, other people, legalities, and so on can force us to compromise or just give in.
Personality Cornerstone
Not staying true to your heartfelt personal beliefs can have a significant long term effect on your well being. Unfortunately, these beliefs might not be widely held by others nor even based on scientifically proven facts.
However, they are ours and however, they were formed by us it is this personal ownership that makes them so powerful.
Our beliefs can, and should, change over time mapping to changes in circumstance but by and large, the basic principles we adopt at a young age will remain intact (i.e., our personal values)
Staying the Course
Accepting cases where others overrule what you believe is right is just a part of living. It does happen. Most important for your own well being is to find a way to accept these decisions without harming your own psyche.
This requires a reasonable level of persistence to influence change to align with your core values and beliefs. That is you must try in a measured and logical way to influence the change.
Reasoned arguments/discussions will help you shape the decision/ imperative in a way that either leads to change or acceptance on your part without remorse or regret.
When seeking to influence change based on your own personal beliefs, remember persistence is critical but not to the point of banging your head until it bleeds.