Nah man sorry. You're just wrong in this case. You're missing the forest for the trees.
Communism was the conspiracy. China. Vietnam. Laos. Cuba. Yemen. Somalia. Congo. Mozambique. Afghanistan. These were the countries succumbing to the worldwide conspiracy he was talking about.
Not to forget that Kennedy increased US involvement in Vietnam to prevent the spread of communism. He sent more troops and military advisers to South Vietnam to fight Ho Chi Minh's forces. His brother also served under McCarthy as his father was a major ally and raging anti-communist.
Also regarding religion, Kennedy was a devout Catholic, which was a massive issue for him during the election, giving him good reason to try and dissuade people from considering it as an issue for him. Back then Catholics were often questioned on their loyalty, with people concerned that the president would be answerable to the pope. Crazy I know.
They've been trying this for decades in Australia. The so called red-unions.
The red unions have never won a bargaining agreement. Have never even won a seat at the table. They've never even won the right to have representatives in the workplace. They're openly sponsored by bosses to muddy the waters and divide actual unions. They are unregistered and undemocratic.
Despite the fact they've never done anything for their members they claim to have 18,000 members. Mostly anti-vaxxers.