Electronic – What circuit will allow reverse polarity and continue to work

There is no reason why a DC polarity reversal should take place, and the warranty can basically blame it on the user.

If the device is battery powered, the use of a standard, convention-adhering battery holder with clear markings should prevent such a thing from ever happening. Even users who don't look at markings are trained to put the flat part of an AA battery against the spring, and slide the nub against the leaf contact. 9V batteries have gendered connectors; no way to screw up short of deliberately making a temporary wrong-way contact while the power switch is on. The 99.999% of the users who are able to engage two brain cells cells together when installing a battery don't want to sacrifice battery life for the sake of the remaining 0.001%.

If the device has an AC adapter, then a polarity reversal can never happen if the original AC adapter is used. If a different AC adapter is used, which has a compatible DC barrel jack, but which puts out opposite polarity, or perhaps AC, that's the user's responsibility. Chances are that by the time users have lost the original AC adapter, the item is out of warranty. Possibly, they are not even the first owners, and so do not have the original receipt. So the chances are low of the company having to replace the item or provide a free warranty repair because of damage caused by a wrong polarity (or voltage, for that matter) aftermarket AC adapter.

Internal DC power supplies that run strictly on AC via an AC power cord obviously have no need for DC polarity reversal handling; the only way it could happen is that someone assembles the circuit wrong.

Consider using an LM311 comparator powered from the available +/- supplies and driving an SSR.

Divide the input voltage down by (say) 11:1 as shown. That gives a 45mV to 4.5V signal at the inverting input of U1 for a 0.5 to 50V input. The non-inverting terminal is held at about 23mV, so input voltages greater than +360mV (allowing for 10mV \$V_{OS (MAX)}\$) will turn the SSR on. Zero or negative input voltages leave the SSR off.

The circuit shown presents a small resistive (11K) load across the input. If that's objectionable, an additional high-impedance buffer could be added ahead of the comparator.

^{simulate this circuit – Schematic created using CircuitLab}

A suitable SSR might be the 60V-rated CPC1907B, which will look like a ~0.06 ohm resistor when it is on and is okay for 3A (6A rating) (a bit more resistance worst-case as it warms up).

The same principle could be used with the comparator driving a heftier SSR, or a mechanical relay, which would allow even lower series resistance. It's also permissible to parallel a few CPC1907Bs with the input LEDs either driven from individual 1K resistors or connected in series with single a lower value series resistor.