Does applying hand sanitizer containing alcohol or its derivatives to the hands before prayer invalidate the ablution and the prayer?

Ablution is not nullified by touching impurities. However, the impurity must be washed off before prayer, because among the conditions for the validity of prayer is purification from both ritual impurity (hadath) and actual impurity (khabath). If you do not know whether the sanitizer contains alcohol or not, then nothing is required of you, and the default status of things is purity.