If Mashek was right, Biden could enlist the government's help to force the bishop to let him receive communion. If that were the case, the government force the Catholic Church (or any other religious body) to comply with any other directive the majority in Congress, or an activist judge, wanted to impose--like requiring the ordination of women. During Prohibition the government could have banned the use of wine at Mass.
Biden is part of the government. If the church has to cater to him, then the "free exercise of religion" is as meaningless in the US as in China or Cuba.