I thought if the DM of a game bought content on DnD Beyond, their players could access it. However, a player told me today that they were trying to make a goblin character, but couldn't see that race as a choice. Did I miss something on my end here? Maybe I don't have the proper type of subscription? Or is it a feature I have to do something in order to implement? Any help is greatly appreciated.

You or one of your players need a Master Tier subscription to unlock the content sharing.

Thanks for letting me know. Is there any way to easily upgrade to one?

I do not know if you can upgrade it, check on here.

Never mind, I think I figured it out. Thanks so much for your help!

When you are in a campaign, you can see all the homebrew of your group, even without a subscription. To deactivate this, go on the first page of the character builder and un-toggle Homebrew Content.

Now, with a Master Tier subscription, go on the campaign page. On the top left, there is now a bow where you can activate the sharing. If you do that, you should be able to see any purchased content of your group (maybe it would take a couple of refresh page to show up).

Needless to say, if your group hasn't bought any non-free content, that content won't be usable.