As someone with an disordered attachment style this behavior isn’t ok. It’s feeding the fear by invading privacy. You can ask for permission. But unless you have genuine reason to suspect something is up invading privacy isn’t ok. People with secure attachment styles may be able to keep going after this, but it’s still a violation of them.

And beyond that, anxious, avoidant, and disordered attachment styles while deserving sympathy are still unhealthy attachment. Secure is healthy. My anxiousness is a burden on my secure wife that I’m actively working on.

If you don’t feel secure in your relationship with someone you need to ask yourself if it’s you or them. If it’s you, you need to be working on it. If it’s them you need to start talking or planning to leave. Invading their privacy isn’t a healthy response to insecurity regardless of whether or not they cheated.