Until now I am very comfortable using trustwallet, there you can store many types of coins. Whether it is safe or not depends on how we treat it, because in crypto there is only one way to break into crypto wallets, namely with a private key, while we keep the private key safe and no one knows it, our assets will be safe regardless of the wallet.
But if it's a wallet provided by a third party, or an app / site provider then I think it's useless if we keep the private key, Because they must know our private key. Better not to use an online wallet if you want to store your Crypto. Use an offline wallet like Trezor or Ledger.
provided by third party doesnt necessarily means they store your privkey but it's indeed safer to generate the private key yourself and not using any third party services but an open source desktop wallet if you want to be secured fully and to note wallet from exchange usually dont give you privkey.