Please have in mind that Tableau is not really designed to to show cross tabs. So in general, some principles that are true for Excel might not be true for Tableau.
However to achieve what you want (not coloring odds or even rows) you can format it to do so. Right click on crosstab> format>Click little bucket on the top and adjust color for Row Banding
sure I understand your point, however not every banality needs to be put into a fancy chart. Sometimes a table is sufficient too.
Of course I know how to change the row branding the way you showed me, but I don't want to do this over and over again for every table I create...
Is there now way setting that option to none for Tableau generally?
I am afraid it's impossible to setup no/white band as default. So now it's a question how many sheets / reports you have because it might be faster to do it manually. You can also try to edit .twb file in text editor and alter line responsible for banding color:
<format attr='band-color' scope='cols' value='#b5ead7' />
<format attr='band-color' scope='rows' value='#b5ead7' />