Is it illegal to use culture symbols on t-shirts that are for sale?

I think I just answered this question with regards to an ankh symbol. You would have to check about the exact "culture symbol," since some such symbols may be trademarked or copyright registered or owned by a group. For example, if you want to use a peace symbol or a cross, as long as it is your own design, then that is fine. If you plan to use a symbol that may be trademarked by a proprietary type church, a fraternal organization, or some such group, you may be violating their trademark or copyright. You should consult with a lawyer. Doing so may be a lot more affordable than you think.

I'm not sure what you mean by culture symbols. To be safe, I recommend contacting the entity and asking for permission to use the image. Many symbols are trademarked and using them without permission is a violation of federal law.