True. It also probably partly comes down to how "foreign" the word looks and seems. "Pest" is an English word and so it may seem reasonable to people to pronounce it in the English way. "Ibiza" on the other hand is very un-English in appearance, and moreover it has only relatively recently come into popular consciousness (unlike, say, "Paris" or "Berlin").
But one thing about language is that it tends to follow its own path and usage is only partially able to be analysed logically.
Rightly or wrongly, I'd have to think for a moment about what a person was talking about who pronounced "Ibiza" without something approaching a lisped sound.
I would have to agree, although I take no offense with others who may choose to use a different pronunciation.
If I'm speaking Spanish and I refer to Mr. Jones or to Milwaukee, I will pronounce the name in English, despite the fact the pronunciation in Spanish would be totally different. Conversely, if one's name is, for example, Iglesias, and one is speaking in English, it would be logical to attempt a pronunciation that approximates the original Spanish.
The fact is that the majority of Spaniards pronounce Ibiza with the lisp, as in Spain not lisping the z is not the majority accent. One can choose to Anglicize the pronunciation of Ibiza or to approximate the original Spanish, but given that it is not a commonly known name in English, and because there is no consensus on an Anglicized pronunciation of the name, perhaps the prudent thing would be to try to pronounce it as close to the common Spanish pronunciation, without necessarily concluding that doing constitutes an affectation instead of a sign of respect for the original language.
We are now at a time in history where we don't necessarily expect names to be translated as they were centuries ago (Cristobal Colón - Christopher Columbus, Jorge Washington - George Washington).