Insurance on investment property, is replacement cost commonly required by lenders?

TLDR: Is it common for mortgage lenders to require insurance with "replacement cost basis" on investment properties?

Background:

I have owned a rental property (3 units) for a few years. Looking to refinance to take advantage of current low rates. Found a bank that offered a much better deal than my current lender. Everything is approved, except the lender does not like the insurance policy on the property. The lender is describing the policy as an "actual cash value" policy, and says that they won’t take it. They only want "replacement cost" policies.

In talking with the insurance agent, the building is currently insured to $350k (I paid $325k for it, loan amount will be ~$240k), but he estimates that to rebuild the same property would cost around $600k. Therefore, to change my policy to a replacement cost policy, he says he would need to raise the premium considerably to cover the difference between $350k and $600k. I understand why he has to raise the premium, but I definitely don’t want to pay that extra amount if I don’t have to.

Further, my insurance agent claims that he has never heard of any mortgage lender requiring a "replacement cost" policy on an investment property, and that "actual cash value" has always been sufficient. Is my insurance agent correct? Is this an extremely unusual request from the bank?

I’m thinking of trying to find another lender, but want to save the hassle if they will all have the same requirement in the end. So far I have only a sample of 2: my current lender is okay with this policy and the proposed new lender is not.