Had a similar problem, now fixed. I have several versions of LO installed on Linux Mint 18.3 so that I can always go back to prior version after installing the latest.
Installed LO 7.1.3 which initially worked fine. Then I removed an older LO version (6.2.?) which broke 7.1.3 but NOT prior versions 6.4 and 7.0.
Symptoms were LO 7.1.3 just puts up the initial splash but then quits a few seconds later. Starting from command line instead of GUI shows these errors:
(soffice:21419): Gtk-WARNING **: Theme parsing error: <data>:1:193: 'min-height' is not a valid property name
(soffice:21419): Gtk-WARNING **: Theme parsing error: <data>:1:209: 'min-width' is not a valid property name
/opt/libreoffice7.1/program/soffice.bin: symbol lookup error: /opt/libreoffice7.1/program/libvclplug_gtk3lo.so: undefined symbol: gtk_widget_path_iter_set_object_name
Fix for me was to add an environment variable with this command line:
export SAL_USE_VCLPLUGIN=gen
and LO 7.1.3 works fine again.
According to this, LO 7.1.3 requires GTK+3 v3.20. Prior LO versions only need v3.18 (which is the version in my Mint 18.3) – explaining why those previous LO versions still worked for me.
EDIT: To make the change permanent I added “export SAL_USE_VCLPLUGIN=gen” to the .profile file in my home directory, logged out and back in again.
This seems to work for now. The better long term fix is probably to upgrade GTK+3 to >= 3.20