No Xbox Live Gold, want multiplayer FPS and racing games (XBox One)

Solution 1:

No, you cannot play multiplayer games without a Xbox Live Gold membership. You will also lose access to games you've acquired with the monthly "Games with Gold" giveaways. Most apps and local split-screen and offline singleplayer games will continue to work.

One of the workarounds to using the multiplayer features of the Xbox One without paying for Xbox Live is to use someone else's account who already has Xbox Live. You cannot both use the same account simultaneously, of course, but it does allow you to play games online if you have a friend who can loan you an account.

User Ryan_L also mentions three alternate workarounds in their answer.