I can hardly understand this sentence:“They confidently sermonize on the fixed nature of identity.” In what kind of context will this sentence be used?

This sentence is an example used in the definition of "sermonize". It is not actually necessary to understand what "the fixed nature of identity" is in order to understand the definition. "To sermonize" means to talk in a particularly dogmatic way about a topic, as if one were delivering a sermon. The speaker will usually only express his own opinion and will do so in such a way as to suggest that it is the only point of view which it is possible to hold. "Identity" means all of the information used to define who a particular individual is and what role they play in society. Identity is considered "fixed" when it does not change. Society is better equipped to handle fixed identity, whereas most people's true identity is dynamic and ever changing. While certain information about us (like the colour of our skin or our eyes or our date of birth) does not change and can be considered "fixed", other things, like the clothes we wear, our jobs and our outlook on life can and do change, sometimes quite radically and frequently. These elements of our identity are "dynamic". Someone who 'sermonizes on the fixed nature of identity' is asserting dogmatically that identity never changes and that a criminal, for example, can never truly change and become a law-abiding person.