I normally go straight to my subscription notifications when visiting BGG. Many of my subscriptions are triggered from Guilds and particular games, rather than threads. Often I can see from the subject line that I won't want to read the thread, but if I just click "Mark Read" it will come back whenever anyone replies. I would find it helpful to have a "Block" button to prevent seeing notifications from that thread in future. This would save clicking through to the thread in order to block it.
If you look at your list of notifications, you should see a dropdown to the left of the thread title. You can click that and select block without needing to go to the thread.
Edit:note you will still need to mark that notification as read, but you should see no more notifications for that thread.