There is no guarantee that stable coins will be safe, learning from experience in the LUNA case, even stable coins can collapse if the main support collapses. I only use stable coins that have been proven to have a strong foundation, such as BUSD and USDT.
Using centralized stablecoins, you must fully trust their issuer. If you fully trust the companies Tether Ltd and Binance, then you can continue to use USDT and BUSD to store your funds. Otherwise, as an alternative to centralized stablecoins, you should consider decentralized stablecoins such as DAI. At the same time, algorithmic ones should be avoided, since UST has compromised them.