Do Taiwan Province compatriots have to buy social security?

According to mainland laws, it should be handed in. If the employer does not help you pay, you can sue according to law.

However, if the employer intends to hire or accept personnel dispatched by Taiwan, Hong Kong and Macao, it shall apply for employment certificates for the personnel from Taiwan, Hong Kong and Macao, and the employees from Taiwan, Hong Kong and Macao who have obtained employment certificates will be protected by law when they are employed in the mainland.

Therefore, I suggest that you ask the unit to help you apply for a Taiwan, Hong Kong and Macao employment permit. Only by obtaining employment certificates can people from Taiwan, Hong Kong and Macao who are employed in the mainland be protected by China's Labor Contract Law.

Article 11 of the Regulations on the Administration of Employment of Residents of Taiwan Province Province, Hongkong and Macao in the Mainland:

The employing unit shall sign labor contracts with employees from Taiwan, Hong Kong and Macao, and pay social insurance premiums in accordance with the Provisional Regulations on the Collection and Payment of Social Insurance Fees.