Are there any rights that absolutely cannot be denied under any circumstance in the United States?
Most rights do indeed have limits where they collide with the rights of others, or the public welfare. But there are some rights that are absolute in US law. Of course these can be violated, but not lawfully. The following are in no particular order.
One cannot be lawfully enslaved in the US, although a convicted criminal may be sentenced to hard labor if a statute so provides.
One cannot lawfully be held in peonage, aka debt-slavery, in the US. (That is a situation where a person who owes a debt is legally compelled to work for the creditor, and is jailed if the person refuses or tries to escape.)
One cannot be lawfully convicted of crime in the US without having been afforded the basic elements of Due Process of Law, including: an independent tribunal; the right to present a defense; the right to present witnesses in that defense; the right to know the charges; the right to competent legal assistance. In most but not all cases there is also a right to a jury trial.
One cannot be lawfully compelled by a government official to take part in a religious observance or service, nor may an adult be legally compelled by anyone at all.
One cannot be lawfully compelled to affirm or deny a religious or political belief.
One cannot have one's property seized without due process of law, although just what process is due will vary depending on the circumstances.
One cannot be lawfully compelled to support a religious organization.
One cannot be lawfully compelled to vote (in a governmental election) for a particular candidate, or indeed at all.
One who is eligible to vote at all in a particular election cannot lawfully be prohibited from voting for a particular candidate. However, if the candidate is later found ineligible, the vote may not be counted.
One may not lawfully be compelled to participate in any sex act.
One may not lawfully be compelled to marry any particular person.
There may be others. There are many rights with are all but absolute, that can only be denied under more or less unusual circumstances, but that I can think of situations in which such a right might lawfully be denied to someone.
People are, of course unlawfully denied rights far too often, but that is not what is being discussed here.