The Bill of Rights applies to states as well as the federal government.
She is suing the Texas Education Agency - which is not only (indirectly) her employer, but her government. Your argument above is predicated on the false premise that her government ceases to be government when you class it as an "employer."
She has the support of the schoolboard and her community with regard to her case on First Amendment grounds. So for those who have only read the above excerpt, please at least read her own argument on First Amendment grounds (from the Wired article). It addresses some of the points people here are making, such as whether a background check is possible without fingerprinting.
Her objection relates specifically to the electronic storage of the thumbpring image, which, let's face it, means it's on file forever.
The religious argument is highly problematic, as that might enshrine Revelations as valid "case law" to cite for others who share her religion. But the 4th Amendment relates to the exact same aspect: This is not an "employer check"; it is a permanent filing of her fingerprint in the already integrated government datastream.
McLaurin’s lawsuit against the Texas Education Agency cites various passages of Revelation, the final book of The Bible:
He causes all, both small and great, rich and poor, free and slave, to receive a mark on their right hand and on their foreheads, and that no one may buy or sell except one who has the mark or the name of the beast, or the number of his name.… Then a third angel followed them saying with a loud voice — if anyone worships the beast and his image and receives his mark on his forehead or on his hand he himself shall also drink of the wine of the wrath of God.… He shall be tormented with fire and brimstone in the presence of the holy angels and in the presence of the Lamb.
Her attorney, Scott Skelton, said his client believes that the computerized fingerprinting, in which her fingerprints will be stored in a database, is the mark addressed in Revelation. The teacher does not believe that it is merely coincidence that Revelation says only those with the ‘mark on his forehead or on his hand’ will be able to buy or sell, since only those teachers who comply with fingerprinting requirements will keep their jobs, he said.
“This law prohibits the free exercise of her religion,” Skelton said in a telephone interview.
The Big Sandy Independent School District, where the woman teaches, is located about 100 miles northeast of Houston. Wayne Haglund, the school district’s lawyer, described McLaurin is a “valued member of the faculty and one of the best teachers we have.”
“The school district’s position is fully supportive of Mrs. McLaurin,” Haglund continued in a telephone interview. “We’re caught in the crossfire. We believe her religious beliefs are sincerely held.”
Haglund said the Texas Education Agency informed him it would deactivate her teacher certification if she does not comply. She has until Nov. 7, Skelton said.
Texas lawmakers approved the fingerprinting measure in 2007 in a bid, Skelton said, “to catch somebody with a criminal background or a history of preying on children.”
“She’s willing to undergo a background check,” Skelton said, “just not fingerprinting.”