Can washer fluid catch fire if accidentally spilled on a hot engine?

A quick search for "washer fluid MSDS" yields a material safety datasheet that lists the flammability limits for methanol as follows:

Lower Explosive Limit (LEL): 6 % (by volume)
Upper Explosive Limit (UEL): 36 % (by volume)
Flash point: 90 °F
Autoignition temperature: 878 °F

So methanol will readily vaporize (flash off) if it comes in contact with a hot surface (90+°F). It will readily ignite without spark above 878 °F. Exhaust manifolds can reach that temperature.

To ignite in the presence of a spark, methanol needs to be within the lower and upper flammability limits, which will be governed by its concentration levels.

Highly unlikely to catch fire. Alcohol level is low , maybe 20 % max. I have added 50 % to water for washer fluid and you get a MUCH stronger alcohol smell in the car than any commercial mix. So there is not enough alcohol vapor to reach the explosive limits in the commercial mix. Dripping hydro carbon onto a hot metal surface has a low risk of ignition. We did a lab test dripping gasoline on a 800 ( +/- ) F steel surface and had no ignition. A spark will ignite it but this is a low risk with modern engines and individual coils ( no bunch of high voltage wires from a distributor leaking sparks ). Warnings such as this are often caused by a single exceptionally unusual case where there was a problem and some lawyer sued somebody. Before your grandfather was born , alcohol water mixes were used in car radiators , this caused fires with large leaks hit the old distributors ( 1940's).

According to the Houghton Chemical website (one manufacturer), "The desired percentage of pre-mixed windshield washer fluid is 37% Methanol which yields a freeze point of –20°F." Although various mixes abound on the market, including summer blends and others for relatively temperate regions of the country, freeze protection of -20 seems to be one of the most common that I've seen in stores. If you used the same rating system as with alcoholic beverages containing ethanol, this translates to 74 proof, nearly as much as the 80 proof for typical vodka or gin, both of which can be set on fire with a little patience.