I can't get it to fault with the behaviour you describe, no matter which Tidy mode etc is used. The only time I see > inserted in the html is when I screw up with my find/replace and am not careful about closing a xml tag. As theducks says I would always replace the *whole* tag anyway, rather than trying to fiddle with the inner contents.
Provide an example epub attachment and exactly what all your settings are to replicate it, though I doubt there is much we can do about it in any case.
Note that there will one day be some changes to how Replace All behaves with regards to "cleaning" afterwards. As has been said many times Sigil is currently very dependent on only working with valid xhtml. In turn the user only gets prompted about stuff made invalid in a tab they have open. In the case of a Replace All operation because you could make html invalid in resources that are not currently open in a tab (using Replace in All Files) it currently does a minimal "clean" after a Replace All that does not happen when you do a manual Find/Replace. This ensures that for instance if you do a Find of "<span class="calibre3">" and a Replace of nothing that it automatically removes the closing matching </span> tags. It can be a very handy "feature" if carefully used, equally you can trash your whole epub with a careless typing in Find/Replace.
It will one day be all tied into the same Clean Source options (a new option is being added for 0.6.1 at the moment) to allow user control of this. However vast amounts of Sigil need changing to fully enable it, there will be tears and pain along the way.