Preliminaries:

Shopkeepers version : 1.7.10 all version, tried latest one too
Cauldron version : cauldron-1.7.10-1.1388.1.0-server`

Shopkeeper not working:

The shopkeeper setup works good and behaves great until I need to trade with it. The trade never happens and the menu exits as soon as I click an item in my inventory. Some other non-op players says that it crashes their Minecraft.

When the trade doesn't happen, when the exit of menu appears. There are no console logs.
I have attached a gif regarding this issue.
https://gifyu.com/image/TkkP

Thanks in advance!!

Shopkeepers is not compatible with cauldron. The last time I checked, Cauldron seemed to have behavioral differences compared to craftbukkit/spigot, that causes Shopkeepers to not be able to identify the open inventory (not able to make sure that the correct inventory is open when you click something), and therefore closing it.
I have no plans to look into explicitly supporting Cauldron (nor any 1.7.10 versions of the plugin).