The reason this issue exists is because we added the Clear-Site-Data, cache header to the log out response some versions back.
We did this because without it if you logout and leave the browser open, anyone can access the same pages you visited in that session (I think it is session based only).
That would allow people to use the same browser and navigate back and see which private messages you were looking at, or private forums and so on.
Clearly, Chrome has a huge issue here. As far as I can work out, there is a severe performance bottleneck, particularly if you have a large Chrome profile. There must be some issue in locating items and clearing them from a large cache.
While there is nothing we can do to workaround that issue, and I don't see a fix incoming from Google any time soon, and the number of complaints about this, we have reversed the change and we will no longer pass the clear-site-data header as of 2.1.5.
As ever, it is imperative that if you are using a shared computer you should log out, shut the browser window and even clear the cache manually if you feel that is necessary. Alternatively, choose to browse in Incognito mode on shared browsers for added privacy.
We'll keep an eye out on this being fixed in Chrome but for now, the behaviour should return to normal.