Percentages that are not close to 0 and 100 can be used as they are. To assess this you compare the SD to the distance of the mean to 0 and 100.
SD < distance => use data as they are
Keep in mind that you still have to check if they are normally distributed when you want to use them in a parametric test.
Percentages close to 0 and 100 have to be transformed because they cannot be normal. Normally distributed data are unbounded and symmetrical.
From statistical viewpoint, it is advised to perform an arcsine transformation, the problem is that nobody uses this in practice. Alternatively you can use:
If you don’t want to transform you can use the beta distribution to model percentages.
Values above 100 or below 0 are not allowed when you transform the data or use the beta distribution. You have to replace them by 0 and 100.
This is a typical example of a chi square test where you compare the observed outcome to the expected Mendelian ratio.