What functionalities are blocked if you don't have a PS+/XBLG subscription?
Solution 1:
Without PS Plus or Xbox Live, you cannot play online multiplayer in Monster Hunter World. This is typical of games with online components. You will only be able to play single-player without a subscription.
Here's some other threads affirming this and here is an article about it.
Monster Hunter World will also require PS Plus or Xbox Live Gold for multiplayer, as confirmed on the livestream.
Event Quests will not be locked behind a subscription (even though technically that would require online functionality to receive). See posts in this thread.