So I've tried multiple times to search for both Dhampire and Dhampir in the search bar yet nothing comes up.

This is despite the fact that I can find two custom content pages of the Dhampir race for 5e D&D on this website simply by googling "Dhampir 5e".

Is something wrong with the search bar? Are we unable to browse custom made content by searching for it?

Those are Unofficial Homebrew Races. They won’t appear in the search bar. 

What the heck is an "Unofficial" Homebrew Race?

A race that doesn't make an appearance in the official core material?

Please explain.

Exactly.

Homebrew races are made by people. Cyb3rmind made one of these races you are talking about. Maybe both.

Actual races are made by WoTC, and UA playtest material. 

You won’t find Homebrew with the rest, as they are not made by the official DnD producers.

So your saying this site purposefully discriminates against people's own homebrew content by making it harder to find in order to promote the official material of the setting produced by Wizards of the Coast?

Nope. It’s all Here. Races, at least. The fact that they made it at all is proof they aren’t discriminating.