Arver v. United States, 245 U.S. 366 (1918), also known as the Selective Draft Law Cases, was a United States Supreme Court decision which upheld the Selective Service Act of 1917, and more generally, upheld conscription in the United States. The Supreme Court upheld that conscription did not violate the Thirteenth Amendment's prohibition of involuntary servitude, or the First Amendment's protection of freedom of conscience.

TLDR, not according to the Supreme Court, though you haven’t been the first to perhaps disagree.