Can A Landlord Require Me To Let Prospective Tenants (strangers) Into My Home All By Myself?

I rent a single family home in California. My lease is up at the end of this month. I told them I was fine with prospective tenants coming to view the property. I assumed that an agent from the property management company or the owner would be accompanying them.
However they have informed me that I am required to "host" open houses all by myself.
I do not know who these people are whether or not they are mentally stable, etc. I would never under normal circumstances allow myself to be alone inside with a total stranger.
I told management that I am 100% uncomfortable with letting strangers in to wander around my home. We have young children too.
I requested that the owner or a rep from the property management company be there of prospective tenants want to see the home.
They wrote back ans said that I am required to do this. Buried deep in the fine print of the lease it said that I would agree to host prospective tenants on tours of the home.
I read throguh the lease before signing but somehow missed this. Is this unethical and dangerous requirement enforceable in any way?
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