Pope Urban VIII's beef with Cassini wasn't over his assertion that Copernicus was right, but rather because Cassini was asserting that which he could not prove.
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So, in this case, the church was on the side of the scientific method.
I find it hard to believe that the Catholic Church then was a proponent of scientific method and would have accepted Galileo's theories if only he'd had evidence.
Even now the Catholic Church (and other religions) do not follow empirical experimentalism. They ignore what the scientific method tells them if it disagrees with their beliefs and dogma. Creationism is a common example amount protestant churches, but the Catholic Church still maintains that a healthy sexuality is unhealthy, that homosexual sexual activity is unhealthy, and that condoms don't work in the fight against HIV/AIDS.
To a scientists, "proof" means 'an experiment that I can repeat that confirms this data', to the catholic church (and many other religions), "proof" can include things you read in your holy book. How could Galileo "proof" his theories to their satisfaction?
The church changes character along with those in power, so comparing the church of then to the church of now is not very meaningful, nor is talking about contemporary church views in contrast to past views.
Pope Urban VIII had at one point actually encouraged Galileo's teachings, but Galileo himself was known to be arrogant and headstrong, having little patience for bureaucracy, and virtually no tact when dealing with others, especially if they disagreed with him.
There are a number of ways Galileo could have approached things:
1. Present both the Ptolemy and Copernicus models, along with the arguments for each.
2. Delay publication until he could build a fully working model, rather than a series of observations and assertions.
3. Defy authority, fraudulently publish, and damn the ignorant fools in power.
Option 1 would have been the best approach, as it would be the least jarring to established knowledge and would provide a wedge for new ideas.
Option 2 would likely stir up controversy at a later date, but would not involve insubordination.
Option 3 was pretty much guaranteed to blow up, much like an employee directly disobeying his boss to his face. Even if he and the pope had been the bestest of buds, there would have been no way politically for the pope to ignore his behavior. (As it was, the pope flew into a rage when he found out that Galileo had published behind his back)
Whereas after Pope Urban VIII the Catholic Church has been willing to change it's dogma based on experiemental evidence? That only happens after most of the world agrees with the experimental results (e.g. heliocentricism).
Presenting both theories just sounds like modern creationist "Teach both theories", i.e. a load of rubbish.
The existing authority will not accept new theories replacing the old until VERY compelling evidence has been brought forth (this happens even today in the secular world, and that's a GOOD thing).
Creationism will have a very hard time displacing the existing accepted scientific body of theory and evidence, as has been seen by their constant failures in the past. But sneaking it in under the radar by "presenting both theories" has gained them more traction than any other strategy they've attempted so far.
What the pope was telling Galileo to do was, in effect, the same thing. Sneak the idea in on the coattails of established "truth", and then it'll be a lot easier to embellish it to fullness later.
So I retract my previous statement that the church was on the side of scientific inquiry. In fact, both cases involve intellectual fraud, in that an idea is not allowed to stand on its own merits, but rather requires political machinations in order to be injected into society at large (but then again, when was that ever not the case?). The only difference is that Galileo's teachings were actually true, and creationism is actually false, but we only have that knowledge with the benefit of hindsight.
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So, in this case, the church was on the side of the scientific method.
I find it hard to believe that the Catholic Church then was a proponent of scientific method and would have accepted Galileo's theories if only he'd had evidence.
Even now the Catholic Church (and other religions) do not follow empirical experimentalism. They ignore what the scientific method tells them if it disagrees with their beliefs and dogma. Creationism is a common example amount protestant churches, but the Catholic Church still maintains that a healthy sexuality is unhealthy, that homosexual sexual activity is unhealthy, and that condoms don't work in the fight against HIV/AIDS.
To a scientists, "proof" means 'an experiment that I can repeat that confirms this data', to the catholic church (and many other religions), "proof" can include things you read in your holy book. How could Galileo "proof" his theories to their satisfaction?