They don't.
Let me break it down for you.
"No State shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States;" - Nothing in the unemployment compensation laws abridges the rights of the worker to quit at any time, or the employer to terminate an employee at any time. Nothing.
"nor shall any State deprive any person of life, liberty, or property, without due process of law;" - No state deprives anyone of life, liberty or property, without due process by having UC available for those who lose their job through not fault of their own.
"nor deny to any person within its jurisdiction the equal protection of the laws." - The laws governing unemployment compensation do not deny any person the equal protection of at-will employment laws. All employees are still free to quit, strike, or otherwise cease work at any time.