Not really sure, but their developer page claims that the wallet is open-source[1]. If it's accurate, then it's definitely a positive thing.
On the other hand, regardless if it's safe or not, it's really not recommended to hold huge amounts on money through a software wallet. 99% of people should always go with reputable hardware wallets.
[1]
https://trustwallet.com/developer/I can see that on
GitHub and the code is often updated, but that should not be a reason yet that it is open source. Or you check the codes and completely verify that they are completely open source? I am not a developer and I can not verify this yet. Let us see other members that know about this to comment before we can decide it to be completely open source or not.
It seems that BTC is the only crypto that has open source wallets, maybe Ethereum too but when it comes to multi wallet I haven't find a wallet that's open source and supports 100s to 1000s of tokens, if I am wrong someone should please drop a name.
Some hardware wallets are open source and support bitcoin and many altcoins.
Trust wallet and metamask are both open source wallet which you can find there github repositories on there official girhub account attached below link. It's true that you can not change address on trustwallet unless you will create new wallet with new seed phrase but metamask supports multiple wallet address using one seedphrase that almost identical to BTC wallet except that it didn't display the total balance on all the wallet address that belongs to the single seed phrase.
Repositories:Trustwallet:
https://github.com/trustwallet/wallet-coreMetamask:
https://github.com/MetaMask/metamask-docsMetamask is a web extension, web wallets are most vulnerable to online attack.