The podcast in question can be found here. Here is a very weak attempt at a summary. I'd welcome edits to correct or provide more detail. I worked backward from the end and didn't listen earlier than the following -- there might be relevant material earlier.
Around 45:30, Alain Connes (I assume) is asked some kind of question which I didn't follow. He brings up topos theory, and gives some kind of explanation of what it is, as "mathematics with parameters" (rough quote). He talks about topos theory's relationship to structuralism and category theory.
Around 48:10, Olivia Caramello is asked some sort of question about the place of topos theory in the mathematical community. She talks about her own passion for topos theory coming from it providing a place for different mathematical subjects to come into contact. She talks about resistance to topos theory (I think I even heard "ostracisme" at some point?) being related to hyper-specialization in mathematics. Around 52:30 she recounts a story of a model theorist spending an afternoon trying to convince her that a theorem of hers was "too general" to be true and trying to produce a counterexample.
Around 53:30, the last question is posed to Laurent Lafforgue, and he speaks about encountering a unique "hostilité" towards topos theory among mathematicians. He mentions talking to engineers who think it could be (rough quote) "the language of artificial intelligence".