Astronomers around the time of Copernicus and Galileo believed the moon was a perfectly smooth crystal whose blotchy features came from either colors or gas right above or right under the surface, or just discoloration on the surface (for reasons unfathomed).

The key point is that under Aristotelean theory it was not seen as being made up of as the same stuff as the Earth — celestial bodies were assumed to be entirely different sorts of things than the world we lived on.

What Galileo did in 1609 was to take several telescopic observations which shows that if you looked at the Moon during several phrases the terminator went across it not as if it was a smooth sphere but as if it had an irregular and rough surface, with like mountains and valleys and craters like you would find on the Earth.

So Galileo was essentially saying, what you interpret as just being colors, I can prove is evidence of it being rough. This was not fully accepted by other astronomers for awhile, who argued that ultimately this was a matter of judgment as opposed to proof, and they also lacked Galileo's equipment (a 20X telescope which was novel for its day).

This is one of those arguments that seems very strange to us today both because we have the benefit of high-quality photography of the Moon (including from its very surface), and also because we have been taught since our earliest days that the Moon is covered in craters and is a big dusty rock. But the next time you look at the Moon, throw out all of that if you can, and ask yourself, if I didn't know anything more than what I can see right now, would I be able to tell if it was a big smooth crystal ball with funny patterns on it, or would I be able to tell those were mountains and valleys? Add to it that the smartest people around at the time would be telling you that it is a big crystal, perfectly smooth, and that nothing made sense unless you understood this.

It is not a matter of "willfully ignoring" the world around them — it is about the fact that there are many different ways to view the world around you, and many different ways to interpret evidence. Christopher Clavius, the top Jesuit astronomer in Galileo's day, believed that what Galileo thought he saw was an optical illusion — that the moon was covered in a transparent crystal and what looked like mountains on its surface were really irregularities under its surface. Galileo came up with something of his own theory of optics to try and show why this couldn't be true, and tried to show that you could use the methods of surveyors (on Earth) to measure the height of the mountains (on the Moon), but for people who were die-hard Aristoteleans these were not especially convincing. This was one of Galileo's many observations that attempted to disprove the Aristotelean conception of the universe (the others were sun spots, the moons of Jupiter, and the phases of Venus), and most could be assimilated into the existing worldview by postulating erroneous interpretation. The phases of Venus were the only observation that could not be waved away easily and it was the main reason the Church astronomers switched from the Ptolemaic model to the Tychonic model (both of which are still geocentric, with the Earth at the center).

For more on this, Kuhn's The Copernican Revolution touches on Aristotelean theory very adequately. There is an extensive academic treatment of Galileo's lunar observations in Biagioli's Galileo's Instruments of Credit.

There's certainly a good bit of evidence for this! It was indeed a shock to see imperfections in the moon.

It's hard to say that scholars would have "willfully ignored the world around them." You've got to remember that early scholarly thought prior to Galileo was based off of Renaissance texts. Much of astronomy was taken from Aristotle, and the Aristotelian view of the heavens held that the Earth was the center, and the moon and planets orbited in perfect circles around it. The heavens were considered perfect, and made of a 5th element referred to as "quintessence."

So this was the accepted viewpoint. Now obviously, casual observations don't line up with this. Mars, for example, when viewed from Earth, appears to lull, and move backwards before finishing its trip across the sky. Scholars were interested in coming up with ways to accurately predict its movement, but these explanations were considered simply mathematical ways to predict the position of the planets (important for planning your holidays, which in late Catholic Europe, there were a LOT of), and were not seen as actually describing the position of the planets. The premise that the moon/planets were made of an otherworldly material, and perfect in nature, was not questioned. It was simply known.

So then Galileo takes a look at the moon through his telescope, and notices that it looks like a solid, physical body, with imperfections. This can't fly, and we're all familiar with the heresy charges. Very little happens in the field of planetary sciences for over a hundred years at this point, until William Herschel manages to make massive improvements in the construction of mirrors, and creates more powerful telescopes. (As a humorous aside, his process involved casting them in horse dung, and required constant polishing for periods of up to 16 hours! His poor sister had to help him relieve himself during these polishing sessions.)

Anyway, Herschel notices that the moon does indeed look solid, and his new telescopes allow him to see mountains valleys, and craters on the moon. In 1790 he published his findings in a report titled "Observations of Mountains on the Moon," which was ill-received at first. However this may be because he went one step further, and stated that the moon was probably inhabited by intelligent creatures. The circular craters, he argued, were too perfectly round to have naturally occurred, and must be artificially created. Some of his sketches even show what appears to be vegetation and forests.

More powerful telescopes eventually disproved this, but the same thing happened with Mars. When Giovanni Schiaparelli looked at Mars and saw what appeared to be a bunch of straight lines, he published his findings and insisted that there were canals and cities on the red planet. This similarly was disproved in 1909 when the Hamburg Observatory pointed its new telescope at Mars.

It would be hard to criticize scholars in the 1600s for their reluctance to accept what seems "obvious" to us now. To the naked eye, the moon doesn't necessarily look like a solid object. Raised in a world where it was common knowledge (even in academia) that the heavens were special. The church certainly preferred this notion, and academics aren't always quick to pick up new ideas. The scientific method was a very new concept, even in Herschel's time. It took the Royal Society ten years to admit that he had indeed discovered a binary star, and similarly another decade before they admitted that his observations that Uranus was a planet and not a comet, were indeed correct.