The short answer
No. In 1611 the leading churchman of the age asked the Church's own astronomers whether Galileo's discoveries were real, and they said yes to almost all of them.
Five questions on one sheet
On 19 April 1611 Cardinal Robert Bellarmine wrote five questions on a single sheet and sent it to the Jesuit mathematicians of the Collegio Romano in Rome, led by Christopher Clavius, the most respected astronomer in Catholic Europe. Were the Milky Way and the nebulae made of stars? Was Saturn three bodies? Did Venus have phases? Was the moon rough? Did four stars move round Jupiter? If you please, he added, you may write the answer on this very sheet.
They answered on 24 April, with four signatures. Venus decreases and increases like the moon; they had watched it. Four bodies move swiftly round Jupiter; they had watched them. Saturn is oval. On the Milky Way they were cautious.
On the moon they held back. They agreed it looks uneven, but Clavius thought the patches might come from denser and rarer parts inside a smooth body, not from mountains on its surface. They confirmed what they had seen and declined to certify what Galileo had inferred.
So where does the story come from?
Galileo spent nine weeks in Rome that spring setting up telescopes in gardens so that cardinals could look for themselves. A friend of his reported a few men who would not look at all. That handful has stood in for the whole Church ever since.
The real difficulty in 1610 was not unwillingness but equipment. Almost nobody had a telescope good enough to see the moons, and Galileo was nearly the only person making them. Even Kepler, who endorsed the discovery at once, had to borrow one to see them.
This site is not connected with the Broadway production of Galileo.