If I put a Furry tag on it but the characters that fit that description don't have sex in a scene, would people feel cheated then?
No, for the paranormal tags I would expect content that fits the tag as central to the story, but not necessarily involved in any sex scenes. Furry specifically would imply at least one anthromorphic animal character.
If there is an openly gay character, would I best serve the work by putting the appropriate tag in there once they discuss their orientation?
Unless the story is tagged no-sex, the majority of readers expect the story to involve sex for any orientation tagged.
f there are racial elements inside, would I best serve the work by putting racial descriptor tags inside after races or racism become story elements?
No. If you look at either the category search or the tag definitions faq those are labeled as "Interracial Elements" not "Racial Elements."
These tags are used to specify interracial parings (involving sex unless the story is tagged no-sex).
Also, the sexual question again attributed to race. Can it be non-sexual race relations?
People looking for specific combinations of racial tags or avoiding them are looking for or seeking to avoid interracial sex.
You have to understand the purpose of the tags. The tags, which are far more important with sex stories than no-sex stories are used by readers to either avoid sexual squicks or find sexual kinks.
If you use the tags in a non-sexual context on a sex story you will lose readers and / or piss readers off.