Is the purpose of washing hands after relations to remove tumah or for cleanliness? The difference being, can one touch their eyes or take a drink before washing?
It is to remove tumah, and not merely for cleanliness. Even tough it is because of tumah we may touch our eyes etc. touching food, as this is only applicable regarding washing our hands in the morning, and not be other times.
O:CH 4-18, Taz 13, MG:A 17, Kaf Hachayim 4-60, Eshel Avrohom Buthachah siman 4, Piskei Teshuvos 4-9, 18.