My only suggestion would be to create a calculated field: lower([the field you're filtering on]), filter on that instead and tell the user to always use lower case.
You could combine this with a parameter box, a calculation to force this input into lower case, and then filter based on the the parameter matching text in the field.
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One approach you could take is to start with a string Parameter, like the attached image. Expose it in your view. Then make a Boolean calculated field like the one in another one of the attached images to this post, which evaluates to TRUE regardless of case for whatever you enter in the Parameter. From there, be creative in how you use the Boolean field, based on how you want to use the results of the search.