Seems like setting the value property of Tabs to false will not show any warning and will deselect all the tabs correctly.
Philip's solution works perfectly, here I am just removing the need for the switch case.
In my case, I only had one tab (Login) where I wanted no tab to be selected since it is a button rather than a tab.
Here's what I did to solve this:
<Tabs value={this.state.content !== "login" ? this.state.content : false} onChange={(event, newValue) => { this.setState({content: newValue}) }}>
<Tab value="home" label="Home" wrapped />
<Tab value="tab1" label="Tab 1" />
<Tab value="tab2" label="Tab 2" />
</Tabs>
on another part of my AppBar I had a Login button:
<Button onClick={(event, newValue) => { this.setState({content: "login"}) }}>Login</Button >
Similarly to Philips's answer, the key is in {this.state.content !== "login" ? this.state.content : false} which prevents Tabs from being rendered with "login" value. Instead, it is given the value "false" which is allowed and does not invoke the warning.