It looks like cdn.libravatar.org is giving a redirect to itself, which redirects to itself, etc.  It's badly broken, but the problem actually is that claws downloading the avatar is done synchronously, and also that the remote failure is not recognised.  I removed the plugin (I'm never putting it back, and I forget how it got enabled) and now mail that took a few seconds to display display instantly.  I have had this problem for YEARS, but I thought it was something wrong with my system.

debug logs follow:

** (claws-mail:41583): WARNING **: 21:27:16.434: failed to load image '/home/user/.claws-mail/avatarcache/402873766c4ff1f51e5dbe89bfa38a82': Couldn’t recognize the image file format for file “/home/user/.claws-mail/avatarcache/402873766c4ff1f51e5dbe89bfa38a82”
libravatar_federation.c:128:libravatar federated domain for domain.com not found
libravatar_federation.c:68:new cached avatar url for domain domain.com: x
libravatar_image.c:159:waiting for thread completion
libravatar_image.c:108:retrieving URL to file: http://cdn.libravatar.org/avatar/402873766c4ff1f51e5dbe89bfa38a82?s=48 -> /home/user/.claws-mail/avatarcache/402873766c4ff1f51e5dbe89bfa38a82

MULTI-SECOND DELAY HERE

libravatar_image.c:111:curl_easy_perfom failed: Number of redirects hit maximum amountfile-utils.c:58:TIMING safe_fclose : 0s074ms
** (claws-mail:41583): WARNING **: 21:27:17.905: could not get image
libravatar_image.c:166:thread completed
textview.c:692:TIMING textview_add_part : 1s473ms
textview.c:658:TIMING textview_add_part : 0s000ms
textview.c:1165:Viewing text content of type: plain (length: 4730)
textview.c:788:TIMING textview_add_part : 0s070ms
textview.c:805:TIMING recursive_add_parts : 0s070ms
textview.c:851:TIMING recursive_add_parts : 0s070ms
textview.c:851:TIMING recursive_add_parts : 1s544ms
textview.c:631:TIMING textview_show_part : 1s546ms
summaryview.c:3823:TIMING summary_display_msg_full : 1s571ms