I'm not sure the two statements are in conflict. If a new discovery fits in with what we already know or what we have predicted, then there is less of a hurdle to being accepted by the scientific community. That doesn't necessarily mean scientists will cut corners or just blindly accept that new discovery, after all some careers are built on tearing down the wok of others, just that it is somewhat easier for the community to roll the new knowledge into what we already know.
By contrast, something that upsets the apple cart of our view of any subject is going to be held to closer scrutiny, if for no other reason than it is something new.
Hmmm, I disagree.
Say we have two sets of circumstances.
In set 1, we have new phenomena that have no established theory to explain them.
In set 2 we have a new phenomena but we also have some established theories that are impacted, say Theory A is contradicted and Theory B is caused to be seen in a different perspective.
In set 2, we would look at testing any theory to explain the new phenomena taking into consideration Theory A to see if we can contrast which theory is true, and with Theory B we might also design tests to clarify how the two impact each other.
But theories to explain set 2 phenomena would be no more 'extraordinary' than set 1.
Y
In fact anomalies are quite ORDINARY in science, and contradictory evidence and theories should never be considered 'extraordinary', as I understand it.
For example the split light experiment contradicted existing theories at the time it was discovered to be an anomaly, and the proposed theories to explain it were not extraordinary at all, except to an instinctive notion of how the universe may work.
We also have the so-called 'Black Swan' phenomena which essentially states that absence of evidence is not evidence of absence. And yet the suggestion that black swans existed prior to their discovery would certainly have been considered 'extraordinary' in 1500. Does that mean 'extraordinary' evidence would have been required by the natural science establishment?
And what is 'extraordinary evidence' anyway? You have to prove it ten times over? The evidence has to be double plus good? What does the phrase 'extraordinary evidence' mean?