User839733648 posted
Hi mariolopes,
Because the textbox in .Net with TextMode="date" only supports the
YYYY-MM-DD format.
I suggest that you could modify your code as below.
protected void Page_Load(object sender, EventArgs e)
{
TextBox1.Text = DateTime.Today.ToString("yyyy-MM-dd");
}
the result:

Besides, the TextMode property generally corresponds to the <input type="" /> attribute (excepting multiline which renders a <textarea />).
ASP.NET 4.x introduced additional values corresponding to new HTML5 input types.
Internet Explorer 11 does not support most of these new input types, specifically it does not currently support the "date" values.
FireFox is also not suitable. But Chrome and Microsoft Edge could work well.
effect on Chrome:

effect on Microsoft Edge:

For more details, you could refer to following link down to History to see what is and isn't supported.
https://www.codeproject.com/Tips/776764/Introducing-Textmode-in-ASP-NET
Best Regards,
Jenifer