This will have a bad impact on SEO if this tag is a tag you want to use for the purpose of delivering content to search engines (it can be mistaken for cloacking).
Ideally, you don’t hide tags that contain content that can be used as a keyword in the search engine, H1 tags for example are usually bad options to hide.
Take a look at the content of these tags and consider if it’s worth just changing your visibility in the search engines.
Had a similar argument here:
https://webmasters.stackexchange.com/questions/54892/can-i-hide-h1-tag-will-it-hurt-seo