I accidentally transferred my Bitcoin Cash to Bitcoin (BTC) wallet in BitMEX! A few days ago, I bought Bitcoin Cash and transferred it to my BitMEX Bitcoin BTC Wallet by accident! This is money that I can't afford to lose! What do you suggest I do?

My conversations with BitMEX:

ME: Hi! Please help me 

I just accidentally transferred my Bitcoin Cash to my BitMEX Account. I didn't realize that it needs to be Bitcoin and not Bitcoin Cash. Can you please reverse the transaction so I can fund my BitMEX account properly? 

BitMEX: Unfortunately, our wallets are not capable of BCH withdrawals without extensive development and time, which means the funds are essentially unrecoverable/frozen at this stage. I have placed your details on a list of users who have deposited BCH, and we will contact you if/when we upgrade our wallets to enable withdrawals. 

Currently there is no ETA on this. 

ME: Are you telling me that the funds are unrecoverable/frozen at this stage, but once your wallets are upgraded, I would be able to withdraw? This means I have not lost my money, correct? 

Other exchanges like BitPay have a feature that allows the option to "clone" the Bitcoin wallet address so it can be retrieved. How come BitMEX doesn't have this?

This is money that I can't afford to lose especially in short term. If lose it, I am going to end up losing everything and probably end up homeless :( :( :( :(

BitMEX: It may be recoverable at a later date, however, we cannot be certain of this. 

Please note what is stated on the deposit page: `Do not send Litecoin, Bitcoin Cash, or Tether to this address! Unfortunately, these networks will accept Bitcoin multisig addresses as valid. Any unsupported coins sent here will be lost.

ME: I did some research and found that it is recoverable by BitMEX. BitMEX has the private keys to access my BTC Wallet on the exchange and your help desk should have a way to fix this. Why is BitMEX not trying to work on this now? Have you forwarded this to your technical team?

BitMEX: Our current wallet infrastructure does not support the new BCH chains and it will take us significant time and resources to access which we do not have right now. I cannot give you an update of time when we may be able to access this for you, but we are looking to try and solve this problem in the future. Please bear with us, this is the reason why we explicitly mention to NOT send us anything but BTC.
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.