I accidentally transferred my Bitcoin Cash to Bitcoin (BTC) wallet in BitMEX!
I'm going to not close this as off topic as OP has already contacted the customer support in question. Instead, I will try to answer why some exchanges/companies have such a stance.

Unlike traditional finance systems, crypto does not really have a refund system. If money is sent out of an address, there is no way to recover it without the receiver's cooperation. Due to this, crypto custodians (companies that hold crypto on behalf of others, such as exchanges holding their users' crypto) must take extensive steps to ensure that a rogue staff member, or someone who is able to gain access to internal systems, is unable to send the crypto to an address not controlled by the exchange.

A side effect of this pattern is that in the normal course of operation, private keys are often completely inaccessible to humans. In exceptional cases such as forks and disaster recovery, there will only be a handful of people who are able to access the raw keys/mnemonics and sign arbitrary transactions needed to recover full operations.

Moreover, such keys are often stored inside Hardware Security Modules, which impose further restrictions on access.

For an exchange such as bitmex, the time, effort, and security risk required to recover BCH from a BTC address for just a few users is likely not worth the engineering or human resources.

Many companies adopt such a stance to avoid compromising their security unnecessarily, and to safeguard funds for all users. Certain exchanges, such as Bittrex, have clearly run into this issue often enough that they have a system in place to recover some cross chain funds. However, that is the exception, not the norm.