The action, involving Southern, Merseyrail and Arriva Rail North, is part of an ongoing dispute over staffing and the role of conductors.
Merseyrail said choosing to strike on the day of the race meeting would damage Liverpool's reputation.
Managing director Jan Chaudhry-van der Velde said the protest would "do immeasurable damage".
Speaking after the company's failed talks with the RMT union, he said the "eyes of the world" would be on Liverpool during the Aintree event.
