Hospice evaluator stressed me out! Do we HAVE to switch hospital beds?

If you OWN the hospital bed then you can keep the one you have.
If the hospital bed is rented then the Hospice probably works with a different supplier of DME.
It is possible that they want a also a different mattress.
I am sure your Mom will not have a problem adjusting.

Once you are enrolled in hospice they provide all needed equipment free. They usually have a contract with a certain supplier . The hospice will usually select the supplier who gives them the best deal because they have to pay for the rental out of the daily allowance from medicare. If you own your bed , as long as it is in good condition you do not need to use the one hospice can provide.
The pick up of existing prescribed equipment will not be removed till the new equipment is delivered.

It depends on how long you’ve had the bed through your PCP. Call the supplier ( name usually on the bed). They will be able to tell you. Medicare pays the rental each month for 13 months and then your mom owns it. If you switch to hospice bed your rental starts over. You may or may not like the new bed. I sent my mom’s first one back. They aren’t all the same. You might like the hospice one better. Hard to know. They aren’t always new ones. So there’s that. Talk to the supplier. They can probably guide you on your area. Once you own the bed the supplier no longer is responsible to service the bed.
medicare.gov/coverage/hospital-beds.html

Yes, Hospice have their own providers. Do you own the bed or renting. If you own, I see no reason why you need to get rid of it. If you are renting, then you save money using Hospice. I think someone said that if u get a bed thru Medicare, Medicare is actually renting it.

Care agencies and companies work with different DMEs, so that's probably the issue.

The hospice company probably has a contract with a different DME than the one supplying beds now.

That happened to us when oxygen use after Medicare required oxygen suppliers to competitively bid. The excellent company we had for some time decided not to participate in the bidding (war), so we had to switch to one of the winners.