It sounds like you are editing your properties in Source Mode? If so, to use #
in the tags property, you need to quote the tag:
---
tags:
- "#example"
---
In Live Preview, the properties editor does this automatically if you type a #
with your tag. (The properties editor is the default interface to properties in Live Preview. If you don’t see it, there is a setting to make it appear.)
If you want Obsidian to recognize tags in property fields other than tags, comment on this feature request: