Yes, someone can read your messages without having the target phone. The risk applies to both iPhone and Android users. They may be able to do this by using special software (spy apps) or hacking skills. Sim swapping, phishing, unauthorized access to your iCloud or Google account, or connecting to an unsafe internet connection can also be means by which someone else can read your text messages.
If you’re not the only one using your Apple or Android phone account, then the greater the chance someone can check your messages. For instance, your relatives or family use the same account on their devices. They could easily read your messages if they wanted to. As such, it’s good to have your own accounts to secure your privacy.