Claim: The ACLU is seeking to have cross-shaped headstones removed from federal cemetaries.
Snopes discusses the issue in depth, explaining how this rumor came to be. It even points to an ACLU website specifically stating that the ACLU is not seeking such a removal:
Why does the ACLU want to remove crosses from federal cemeteries?
The ACLU has never pursued the removal of religious symbols from personal gravestones. In fact, following lawsuits filed by the ACLU and the Americans United for Separation of Church and State, the Department of Veterans Affairs agreed to allow family members to include a religious symbols on headstones.
The ACLU has long argued that veterans and their families should be free to choose religious symbols on military headstones – whether Crosses, Stars of David, Pentacles, or other symbols – and that the government should not be permitted to restrict such religious expression in federal cemeteries.
Personal gravestones are the choice of the family members, not the choice of the government. The ACLU vigorously defends peoples’ freedom to choose the religious symbols of their choice. The right of each and every American to practice his or her own religion, or no religion at all, is among the most fundamental of the freedoms guaranteed by the Bill of Rights.
I can’t find anything about the ACLU trying to prohibit military chaplains from using Jesus’ name in public prayer, but it sounds odd; what public prayers are involved? The ACLU has written to the Naval Acadamy to protest mandatory prayer at the noontime meals, but that was a protest against prayer per se, not against a specific type of prayer.
According to The Washington Post, there was a federal investigation of the Air Force Academy because various officials were proselytizing their evangelical Christian beliefs; but the investigation took the form of “You shouldn’t be promoting your beliefs against the cadets’ will,” not “You can pray, just not to Jesus.”