Rights are never in conflict. That's right - NEVER.
The U.S. Constitution was based on Locke's theory of rights as inherent in man, granted by God and not by government. We understand that "rights" granted by government are merely temporary privileges which the government may give and take away as it pleases. (As such, we have no "right" to drive, but it is correctly referred to as a privilege which government chooses to grant or not to grant to individuals, and may suspend or revoke.) Nothing which must be licensed can be a right. Nothing given by government is a right. "I have a right to nothing which another has a right to take away." --Thomas Jefferson to Uriah Forrest, 1787. ME 6:388, Papers 12:477
Rights cannot exist in the absence of property. I do not have the right to walk into your home uninvited and preach the merits of capitalism to you, because you have the right to tell me to leave. Why? Because it is your property. I can, however, speak freely in my own home, produce newspapers and sell them to others, and use my computer to post my thoughts online. Likewise, you are able to use the resources you have earned to obtain newspapers, religious books, and other sources of information. Freedom of speech, freedom of religion, and freedom of the press follows from the right to property.
If I do not own my life and am not allowed to earn and keep the property I need to preserve it, I do not have a right to life. The right to life follows from the right to property.
Without the right to property, I have no right to pursue my own interests because I am incapable of keeping the salary I have earned and using it to obtain other things that I value. If the government or any other group of individuals is able to take my salary that I spent a year of my life working for, they have enslaved me for a year because I was unable to keep the product of my labor for that period of time. The right to liberty follows from the right to property.
Violations of others' rights cannot be a result of inaction. I cannot passively take someone's property or life or liberty. From this principle, it follows that rights are not entitlements. I have no "right" which presents an obligation to another. I do not have the "right" to healthcare. I have the right to earn property which I can use to pay for my own healthcare. You are not "violating my rights" by not paying for my healthcare. However, if I were unable to afford healthcare and you had the obligation to pay for mine, that would violate your right to property. I do not have the "right" to a job because you do not have the obligation to hire me. I do have the right to freely exchange goods and services for money or other property in a free, uncoerced exchange. That is, there is no such thing as a "positive right," or a right to something that requires action by another. If one person's "right" violates that of another, rights are not absolute and are no longer rights. The right to property is a negative right -- when I say I have the right to property, it means that I have the right to earn, keep, use, sell, give away, or dispose of property that I own; no one has the right to restrict it or take it from me. To have both negative rights and positive "rights" is like saying "I have the right to be left alone" and "You have the right to bother me." Simultaneously, they cannot exist.