Texas withholding for other states

I live in Oklahoma, but work in Oklahoma and Texas. Just this year, my Texas employer (University of Texas System) says they must start withholding Oklahoma income tax.

I have had extra Oklahoma taxes withheld  from my Oklahoma job for years to cover my Texas earnings.

How can I avoid having the Texas employer withhold Oklahoma income tax?

Lots of allowances on the Oklahoma W-4? I don't seem to be eligible to write "Exempt"