This is currently not supported directly. There are a couple of potential workarounds:
Use the Preview fields titles toggle to hide the fields' titles from the cards. That way, empty fields won't be so apparent.
Use a formula field to combine 'optional' data and display that formula field in the cards instead of the original fields (see this help article). This is useful if you have a field, or a few fields, that always have data in them, and you want to just add more bits of information that are optional.
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Example: Field Location is always filled for every record, but field Room is optional. You can combine the two into one formula:
â{Location} & " " & {Room}
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Then use that formula as a custom preview field so it will display something like "Office 2A" in the cards. If the extra space shown when the Room field is empty is an issue in your use case, you can always use anIF()statement in the formula based on whether or not the Room field is empty or not.