How can a third party spend BCH accidentally sent to a BTC address? I transferred BCH to an Electrum wallet address and haven't ever received it because Electrum uses only BTC. As I have been trying to recover it, I looked up the transaction on explorer.bitcoin.com and it was input but has also been output 5 times and the  balance shows 0. So it would appear that someone has access. How is that possible? Shouldn't it be secure? Do I have any sort of recourse?
So it would appear that someone has access. How is that possible?

Excellent question
Segwit addresses
Segwit increases the capacity of the Bitcoin (BTC) network and enables the lightning network. Segwit addresses start with 3 or bc1.
On 21 November 2017 Kai Sedgwick reported on  Bitcoin.com

Someone Just Helped Themselves to $600k of Bitcoin Cash from Segwit Addresses
As anyone with a passing knowledge of bitcoin cash will tell you, BCH and segwit don’t mix. Send BCH to a segwit address and you’re gonna have a bad time. Unless you happen to be a miner with the hashpower and technical prowess to unscramble the mess, in which case you’re gonna have a very profitable time. 493 BCH worth $610k has just been retrieved in that manner by one enterprising individual.

A segwit address is just a particular kind of Bitcoin address being introduced as part of some Bitcoin improvements.
Non-segwit addresses
For a third-party to spend bitcoin-cash (BCH) sent to a non-segwit bitcoin (BTC) address, they would need access to the private-key from which that address was derived.
This might happen through the use of viruses, Trojans, fishing or social engineering etc.


Receiving address I have is 19EsSXxaTParaHqQ7V8o9A9xbZ47fApe7f

(from comment to Problems recovering BCH accidentally sent to BTC address)
Blockchain explorer websites show no transactions for that address
Example for BTC blockchain:
Summary 
  Address   19EsSXxaTParaHqQ7V8o9A9xbZ47fApe7f 
  Hash 160  5a6084e7e05b44c3805b8372462e876447b28d43 
Transactions 
  No. Transactions  0    
  Total Received    0 BTC    
  Final Balance     0 BTC

Example for BCH blockchain
Address
     bitcoincash:qpdxpp88upd5fsuqtwphy33wsajy0v5dgvkmjdckhh 

Balance: 0.00000000 bch
Total Received: 0.00000000 bch

Example 2 for BCH blockchain
Address 0 BCH
Address bitcoincash:qpdxpp88upd5fsuqtwphy33wsajy0v5dgvkmjdckhh
Summary confirmed
Total Received  0 BCH
Total Sent  0 BCH
Final Balance   0 BCH
No. Transactions    0


Security

Shouldn't it be secure?

Only if you send Bitcoins to bitcoin addresses and bitcoin-cash to bitcoin-cash addresses.
Groups of people developing different cryptocurrencies don't always cooperate with other groups to prevent this kind of consequence. The split between Bitcoin and Bitcoin cash was a little acrimonious.

Recourse

Do I have any sort of recourse?

No.
Cryptocurrencies are essentially designed as peer-to-peer currencies with no regulatory oversight and with no third parties enabled to intervene in disputes.
You dropped some coins on the floor and someone picked them up.
You could ask the person who found your BCH if they will give them back to you for a 30% bounty. It may be hard or impossible to work out who has your BCH and how to contact them. You will be relying on the kindness of a stranger.
You could report the matter to your local police.

Third Party Oversight

This is me transferring my coins to my account but because they aren't dollar bills the bank teller steals them!

There are no bank-tellers in Bitcoin.
You accidentally sent your bitcoins to the wrong destination. Other people who are unscrupulous can often take advantage of any mistakes you make.

Prevention

Something needs to be done about this


You need to be more careful.
If you ask them, wallet developers might consider changes to their wallet software that might make this kind of error less likely.
I believe the Bitcoin-cash (BCH) developers plan a change in address formats to avoid them looking like Bitcoin's (BTC) Segwit addresses.


Risk.

There is a serious flaw in the cryptocurrency system if it simply allows thieves to pray on people who are new to it without any recourse

Bitcoin transactions are by design irreversible. Bitcoin is a very risky investment. Anyone getting involved needs to take the time to understand the risks before getting involved.
Thieves will always prey on those who make careless mistakes. The nature of cryptocurrencies is that they are conceptually unlike the currencies and financial systems that people were previously used to, this makes cryptocurrencies relatively dangerous for the unprepared. For example, the use of the term &quot;wallet&quot; is misleading because cryptocurrency wallets do not really contain any money. Thinking that Bitcoins exist in the blockchain or are entities that are stored somewhere electronically is an error. This makes it easy for the unprepared to make mistakes and lose money.
Caveat Emptor.

Other useful references

Bitcoin Cash Locked in SegWit Addresses: A Recovery Workaround Discovered