Tread carefully, warily, etc.
Definition 1 of 3

Professional Settings
Use 'tread carefully' when in discussions at work or on serious topics to show you're being considerate.

In negotiations, it's wise to tread carefully with each proposal.
Emotional Sensitivity
Emphasize your awareness of someone's feelings using 'tread carefully'.

After her loss, I tread carefully when mentioning anything related to the topic.
Avoiding Offense
It suggests that what you say next is with the intent to not offend or cause issues.

Tread carefully, but I think there could be a mistake in the report.
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