I encountered this sentence in an anime 素で無視してたー！ I've looked up 素 with jisho, but non of the definitions seem to fit.
Could someone please explain how 素で works in this sentence and provide me with some other example sentences that would be super helpful.
This 素 is read す (not そ), and its basic meaning is "plain". See the second definition on jisho.org. By extension, 素で can mean "without hidden implication", "with a straight face", "without joke/wit/excitement/role-play", "innocently", "seriously", "literally", and so on, depending on the context. In your context, I think the speaker is saying they didn't ignore something out of malice or intent; they ignored it inadvertently.
