So races you buy don't become part of the character builder?

They should. What did you buy? Maybe you need to toggle a character setting.

The Tabaxi. I also created a race but neither show in the character builder.

Tabaxi is not showing up as a race option for one of your characters (not someone else's)?

Is it still not showing up (sometimes there is a 10 minute delay)?

Have you tried refreshing the page?

Is your homebrew race in you homebrew collection (not just creations)?

Is your homebrew race set as (or set to have) a subrace?