These are quotes from his own website:
'A Republic, If You Can Keep It’ by Dr. Ron Paul, U.S. Representative from Texas
Address to the U.S. House of Representatives delivered on the Floor of the House January 31 - February 2, 2000
....The modern-day welfare state has steadily grown since the Great Depression of the 1930s. The federal government is now involved in providing health care, houses, unemployment benefits, education, food stamps to millions, plus all kinds of subsidies to every conceivable special-interest group. Welfare is now part of our culture, costing hundreds of billions of dollars every year. It is now thought to be a "right," something one is "entitled" to. Calling it an "entitlement" makes it sound proper and respectable and not based on theft. Anyone who has a need, desire, or demand and can get the politicians' attention will get what he wants, even though it may be at the expense of someone else. Today it is considered morally right and politically correct to promote the welfare state. Any suggestion otherwise is considered political suicide.
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....Controlled curricula have downplayed the importance of our constitutional heritage while indoctrinating our children, even in kindergarten, with environmental mythology, internationalism, and sexual liberation. Neighborhood schools in the early part of the 20th Century did not experience this kind of propaganda.
....It is now accepted that people who need (medical) care are entitled to it as a right. This is a serious error in judgment.
...Probably the most significant change in attitude that occurred in the 20th Century was that with respect to life itself. Although abortion has been performed for hundreds if not thousands of years, it was rarely considered an acceptable and routine medical procedure without moral consequence. Since 1973 abortion in America has become routine and justified by a contorted understanding of the right to privacy. The difference between American's rejection of abortions at the beginning of the century, compared to today's casual acceptance, is like night and day. Although a vocal number of Americans express their disgust with abortion on demand, our legislative bodies and the courts claim that the procedure is a constitutionally protected right, disregarding all scientific evidence and legal precedents that recognize the unborn as a legal living entity deserving protection of the law. Ironically the greatest proponents of abortion are the same ones who advocate imprisonment for anyone who disturbs the natural habitat of a toad.
....The welfare system has mocked the concept of marriage in the name of political correctness, economic egalitarianism, and hetero-phobia.
....Any academic discussion questioning the wisdom of our policies surrounding World War II is met with shrill accusations of anti-Semitism and Nazi lover. No one is even permitted without derision by the media, the university intellectuals, and the politicians to ask why the United States allied itself with the murdering Soviets and then turned over Eastern Europe to them...'
So let's see. Paul is totally against any form of welfare state, even in its current American sense (very limited compared with most other developed countries); considers benefits for poor people to be 'theft'; does not think that people are entitled to medical care. Despite all his libertarian justifications for all the above, thinks that the government is entitled to ban abortions and 'defend marriage', (though he considers that these, like other government functions, should be carried out by individual states rather than the national government). He is opposed to gay rights ('heterophobia') and considers concern about the environment to be based on 'mythology'. Moreover, he is so isolationist or anti-Soviet or both, that he would apparently rather have had Hitler take over Europe than have an alliance between America and the Soviet Union during the war.
Here's a link to an essay in my journal, from which this is taken, which I wrote about three years ago, and which goes into more detail about what is wrong with Paul, why this matters even to a non-American like me, and the dangers of collaboration with right-wingers.
http://journals.democraticunderground.com/LeftishBrit/29As regards racism in particular: Paul certainly seems to think that states should have the right to practice racist policies as part of 'states rights', and has expressed opposition the Voting Rights Act for that reason. He is popular with racist groups such as Stormfront. He may or may not be personally racist; this is less important than that, if given power, his policies would *enable* racism.