This is not arduino but as I said I know nothing about picaxe; but if it was arduino, digitalRead() takes about 5μs. At 4 reads per cycle, 20μs plus whatever else, IDK, I'll say 30μs.Correct. It's reading or scanning the inputs from 1 to 4. Possible car 1 could cross the line before say car3 depending on which line of code the program was at but it would be within micro seconds.
I assume this is about pinewood derby cars..
According to this website:
10mph = 176 in./sThe actual speeds hover around a more modest 10 mph
(4470mm/s)
(4.470mm/mS)
(0.00470mm/μS)
×30μs = 0.1341mm
That's nearly 3 whole pubic hairs.
Further according to the same website:
The chart doesn't have enough resolution to say conclusively what the time difference is between cars but look at for example car #26 vs car #27:Six tenths of a second. That is all that separates the slowest car from the fastest! (Out of 37 cars)

3 pubes might actually matter.
With arduino there is direct port manipulation where you can read 8 inputs at once in 62.5nS. If picaxe has a similar function then i would suggest using it. Or if it is just blazing fast without the overhead of arduino's padded corners then disregard.