How do I get Kate to line up the columns in tab separated files?

You can try fiddling with the tab width in Settings -> Configure Kate -> Editing -> Indentation. How well that will work depends on how well your data will fit within certain tab sizes.

If that doesn't work, a couple of alternatives include using a spreadsheet app like Calligra Sheets, LibreOffice Calc or Gnumeric which should handle importing (and exporting) your tab-delimited data, or using a word processor app like Calligra Words, LibreOffice Writer or AbiWord which allows better control over tab stop positions.