Is it wise to keep some savings in a cash account to protect against a long term market crash?

Yes, this is the point of an emergency fund.

That depends on what your savings are and what you mean with emergency. If you are having serious investments into stocks and real estate - then your stocks and / or a prepared loan from the bank can handle every emergency you can think of without taking time.

You are right with the index funds - 6 months emergency is good to have, but then you STILL eat into your savings. But this is not a well balanced portfolio. Stocks, some Bonds for what you need in the next 5 years, some Gold (inflation hedge) and some Crypto and you are going to be a LOT more stable.

The bonds are for selling in the next years (so they do not fluctuate too far). If you are well off (i.e. a portfolio with a market cap of 25x your expenses) just rely on an emergency credit line.

Our thinking is that, if there's a long term market crash (e.g. Great Depression) and the value of our index fund plummets,

People were having these exact same thoughts 10-11 years ago after the market fell due to the bursted real estate bubble.

and we happen to have no job income for years, we'll need money to tide us over.

Only making yourselves more employable will truly solve that problem.

Will having savings in cash make our financial situation more secure, or is this thinking wrong-headed?

(Where did you put that cash? Checking or savings account paying 0% interest, a "high"-yield savings account or set of CDs paying -- currently -- 0.65% interest? Bonds? What kind of bonds?)

Enough cash to pay for an emergency or keep you afloat until you get a new job is always right-headed.

A mix of cash in a high yield savings account (I like Ally Bank), staggered CDs (Ally is my go-to for them, too) and bonds (TIPS, T-bills, munis, and possibly corporate) is the standard mix.

The basic problem with keeping a lot of cash in the bank is that it slowly disappears with inflation.

(I'm not even mentioning "cash in the mattress" because that is wrong-headed.)

Bottom Line

The wisest things to do, whether or not there's another great depression, are:

1. Get out of all debt (except for a modest mortgage), and
2. Live modestly.

It's wise to have some savings available for emergencies. AFAIC, 1/2 of your savings in an almost zero interest rate account makes no sense whatsoever.

It's up to you to decide you investment/cash allocation but I would suggest that you put a large amount of your cash allocation in a high yield money market account. High yield might be a contradiction of sorts since 60-70 basis points or so (0.6 to 0.7 pct) isn't much but it's a lot better than zero.

If you're willing to be proactive, you can get cash bonuses from some banks when you open a new account with them. I've seen advertisements for yields as high as 13.3% which is a lot better than 60-70 basis points.

It's true that cash is a poor investment because it loses value over time through inflation. But that's not the only problem. It's not even that much of a safe asset and it's similar in risk profile to your safe portfolio of bonds. While rare, currency crashes and hyperinflation are some of the most destructive economic events a country can face and they'd wipe out more of your cash and bond portfolio than a stock market crash would wipe from a stock portfolio. You can find many examples online, such as the recent inflation in Venezuela or in the early 90s for the USSR.

Gold, commodities, and domestic and particularly foreign stocks and real estate are a good way to protect against these potential problems. Each of those have their own issues of course, but if you're playing it safe diversity is the name of the game. There's no completely safe asset.

If you are planning for a "Great Depression" or "end of the world" type scenario, nothing beats having some physical gold and silver.

Precious metals (gold and silver coins) are easy to purchase and sell, easy to store, and hold their value if an economy goes bad.

Buy some coins, own them physically yourself (dont buy into any "good pool" or "hosted gold" schemes) and bury them in a lock box hidden in your loft / garden shed / roof of your cleaning closet / etc ...

Imagine that in a great depression situation, you can always trade a silver coin for some food. A cash savings account in a bank won't help if the banks are closed and the ATM's dont work... ;)

If you are interested, read about economic depressions in other countries in recent years (for example, Venezuela) and how ordinary citizens protected their wealth and safety.

You talk about putting 50% of your savings in a cash account but I would argue this is the wrong way to think about it. The question you should be asking yourself is what are your non-discretionary expenses per month and how many months of expenses you want to cover.

Typically, recommendations range from 3-6 months of expenses. Too much beyond that and your long-term investment goals may be at risk. The main point here is to be able to avoid cashing in investments when their value is down such as during a financial crisis. Even if there is no crisis, you might need cash fast. For example, I just refinanced my mortgage and due to timing, I was required to cover part of my property taxes with cash in order to close. I came out basically even when I received the balance of the escrow on the old loan but if I didn't have that cash on hand, things could have been really messy.

If you are looking at a longer window, there are options for more stable investments that are less liquid but earn more than a saving account such as CD laddering. The next option would be things like high-quality bonds but that is a whole topic on its own.

As a simple plan, divide your money/assets into 3 categories.

1. 3-6 month emergency fund. (Liquid and Accessible)
2. Need access to within 5 years. (Preserving)
3. Do not need access to within 5 years. (Growing)

The third is long term investments (good track record mutual funds and index funds). Over the long term, the stock market goes up.

The second is for money that you are planning to spend within the next 5 years. While, over time, the stock market has always gone up; over shorter periods it is a roller coaster ride. If you plan to buy a house in 4 years, you don't want a market drop just before you plan to buy to wipe out 40% of your planned down payment. It is more important that this money is preserved rather than needing to grow, though some growth is still nice. Compare high yield savings, CDs, and Bonds to find a place to park it. For your example, the money for your living expenses comes from this category. As you use it up, you refresh it from the third category. Just don't refresh it during a downturn. This is your buffer against the roller coaster.

The first needs to be very accessible. This is "insurance" in place for unexpected expenses. You need to be able to access it quickly. Park it in a Savings Account or Money Market. Any interest earned is gravy, but this money is meant to prevent you from needing to cash out other assets, rather than making money itself.