> Would it solve your problem when your mode (locally) binds
> `mouse-1-click-follows-link` to nil?

No, in this case mouse-1 does nothing but relocate point.

I Git bisected the regression to:

25573f61f9eaf1631c03d16486ffc17fd9b18503 is the first bad commit
commit 25573f61f9eaf1631c03d16486ffc17fd9b18503
Author: Stefan Monnier <monnier@iro.umontreal.ca>
Date:   Fri Mar 8 23:15:53 2013 -0500

    Separate mouse-1-click-follows-link from mouse-drag-region.
    * lisp/mouse.el (mouse--down-1-maybe-follows-link): New function.
    (key-translation-map): Use it to implement mouse-1-click-follows-link.
    (mouse-drag-line, mouse-drag-track): Remove mouse-1-click-follows-link
code.
    (mouse--remap-link-click-p): Remove.
    * src/keyboard.c (access_keymap_keyremap): Accept nil return value from
    functions to mean "no change".
    * src/keyboard.h (EVENT_START, EVENT_END, POSN_WINDOW, POSN_POSN)
    (POSN_WINDOW_POSN, POSN_TIMESTAMP): Be careful since events may come
    from Elisp via unread-command-events.