The fact that the purchase in your IRA is done automatically doesn't make any difference. A purchase is a purchase. The purchase being made automatically does not avoid the wash sale rule.
But there are two other questions here.
1. Is the S&P 500 mutual fund "substantially identical" to the S&P 500 ETF?
2. Does a purchase in your IRA make the sale in your taxable account a wash sale?
On the first question there is no clear IRS guidance, and experts may disagree. But there's good reason to consider them substantially identical, since they track the same index. If you compared the price movements of the two funds, you would not see any significant difference. Obviously the safe, conservative position is to consider them substantially identical.
For the second question, the rules are clear that purchasing substantially identical securities in your IRA does make the sale in your taxable account a wash sale. So you cannot deduct the loss on the portion of the fund that you sold that was replaced by the shares purchased in your IRA. What's worse is that you get no adjustment in your IRA for the disallowed loss, so you never get to deduct the loss. If the sale and purchase are both made in taxable accounts, the disallowed loss is added to the basis of the replacement shares. That means that when you eventually sell the replacement shares you get the benefit of the original loss. Your gain on the sale is reduced by the amount of the wash sale loss. But when the replacement purchase is in your IRA you never recover the disallowed loss from the wash sale.
In your specific situation, neither the purchase being made automatically, nor the purchase being in your IRA, avoids the wash sale rule. So the question comes down to whether the S&P 500 mutual fund is "substantially identical" to the S&P 500 ETF. The safe position is to consider them substantially identical and exclude that portion of the loss.
For an excellent, very detailed discussion of wash sales, see the following link.
The Wash Sale Rule
