Liberals disagree internally amoungst themselves about the idea of Natural rights and equal moral worth. One of the main thinkers that focused on the idea of natural rights is John Locke, he based his beliefs on this idea. For example Locke believed in the idea that Government had to be established by consent and therefore respect the natural rights of citizens. Natural rights are believed to be given to us at birth, rights that are granted to each individual by God or by nature. However there are disagreements and other Liberals believe in the idea of rationalism, and they cannot see any reason for there to be inequality or elite people within society, they believe that inequality is un-natural and isnt a part of human nature and they do not believe in the idea of one individual being more powerful than that of another, however both agreeing with the idea that we are all created equally.
However, although Liberals believe in equality of rights, a large majority of liberals also agree that each individual varies from skills, talents, and abilities and therefore do not believe in equality of this sort but the belief of every individual coming together with the same goal of succeeding to their full potential and acheiving self fullfillment. This therefore follows up to the idea of equality of outcome, believing that inequality of outcome is acceptable on the condition that is a result of different skills and therefore acheiving different goals as skills and talents vary from person to person.
For example an individual more talented than another may earn a larger amount of money than that of someone less skilled however this is considered a natural occurance within society and is therefore accepted. This goes against the ideas of socialism where it is universally believed that everyone is born with equal potential of intelligence and therefore believe that inequal is a result of inequal treatment by society. However although Liberals believe that their may be inequalities of wealth due to this variation of skills, they do believe in the idea of taxing the rich with an aim to provide welfare to those that are a lot poorer in an attempt to balance out the large scale differences in society to enable a more comfortable living quality for those who may be less skillful than others.
Another kind of equality in which Liberals believe in is that of equality of opportunity. Initially the classical Liberals (19th century) believed in the idea of individual liberty, individuals were free from any restrictions to their freedom and were given the opportunity to choose their own outcome, whether it be wealthy or poor, success or failure. However this method did not seem to be effective and had numerous problems.
J.S Mill realised the problems with his philosophy also. However a new Liberal party had been formed and offered a more effective way to create equality of opportunity. It enabled class differences to become more equal, the lower classes were offered the chance to enter into professions such as Law and the army which they had previously been restricted from doing in the older system and therefore a wider majority of society were enabled to engage in similar activities and therefore had more equal chances to earn rewards. Equality of opportunity recognises that some individuals may be unable to achieve as much as others and establishes thats individuals are born with disadvantages that cannot be overcome despite their hard working efforts (such as disability).
Equality of opportunity also promoted through education (universal) and therefore elementary education was enforced for all classes and equality of opportunity was further implimented through welfare state, education, healthcare and social security (policing etc) and therefore no matter if someone were disadvantaged at birth they would still be entitled to the same opportunities and rights as a human being.
Therefore in conclusion, equality within Liberalism may have had inside disputes however it is acknowledged that Liberals universally believe in the idea that every individual is entitled to equal rights. Liberals believe in different types of equality to ensure that all sections of society have the same life chances as one another, to enable a good quality of life for all despite differences at birth and to enable every individual to achieve their personal goals by providing them with the opportunity to do so, no matter what their social class.