how does the language of the equal protection clause show intention to safeguards all groups' civil liberties

Answer: It is describing life, liberty and property protection for all citizens

Explanation: The Equal Protection Clause of the Fourteenth Amendment prohibits states from denying "any person within its jurisdiction the equal protection of the laws." - This is missing in your question.

Intention to safeguards of all groups is shown with the phrase ''any person ... ''. It is referring clearly to all people and it isn't mentioning gender, religion, race, education or something else. The key of it is to protect all of the people and everyone should be equal. It is also put to protect African-American citizens which were having issues with discrimination trough the history.

''The equal protection of the laws.'' is referring to a protection that is equal with all aspects of life, property and liberty.