There is a famous reference in the so-called Galileo affair to various people refusing to look through Galileo’s telescope at the sunspots and other phenomena he wished to show them. The best known is Cesare Cremonini and I did some digging to find a reference, locating it in the Opere, II, 564, which is a letter from Paolo Gualdo to Galileo. Cremonini had discussed Galileo’s work with Gualdo and said that he wouldn’t be considering it in his new book (the Disputatio de coelo). Cremonini’s words were thus:
I do not wish to approve of claims about which I do not have any knowledge, and about things which I have not seen … and then to observe through those glasses gives me a headache. Enough! I do not want to hear anything more about this.
To understand why he was not interested we have to look at his position at Padua and the role of Aristotelianism. Cremonini was a great friend of Galileo but at that time Peripatetic ideas were under threat from the mathematisation of natural philosophy and Cremonini was nothing if not a thorough-going Aristotelian. He had obtained his position through study rather than the Court, and he was paid to teach Aristotle (in fact, he said when under investigation by the Inquisition that he would have to return his pay if he declined to teach Aristotelianism). More generally, according to Aristotle the heavens were supposed to be incorruptible and hence there could be no sunspots, so why look through a telescope? Cremonini’s reasons were thus philosophical and ruled out Galileo’s observations a priori, so there was no need for telescopes.
The other case is Giulio Libri and the only reference I could find is Galileo’s letter to Welser of 17 Dec 1610, in Opere, XI, 14, in which Galileo remarks on the recent death of Libri by saying that “never having wanted to see [the Medicean Stars] on Earth, perhaps he’ll see them on the way to heaven?” Libri was an opponent of Galileo’s, so this was a somewhat snide comment. His reasons appear to have been more practical: in his book Natural Magic of 1589, Giovanni Baptista Della Porta had shown that all manner of optical illusions were possible, and although people could use the telescope to view something terrestrial and confirm that it was accurate, there was no guarantee and no theory to account for doing so with the heavens. Moreover, at the time of Galileo no complete theory of optics was available to distinguish between genuine effects and tricks or self-deception, so it was necessary to be at least a little skeptical. However, this seems to be the only source on Libri - from Galileo, an enemy.
The interesting thing about all this is that there are plenty of references in the literature to these refusals but hardly any documentation supporting them. Most historians simply recounted the story as something that had long ago passed into Galilean lore or else referred to someone else’s doing this in an earlier history.