uLoL

Believe it or not, uLoL does not have a rank requirement to participate. This is documented in their 2017 Rule Book:

Players must have a League of Legends account in good standing and eligible for ranked games in order to compete. This same account must be used for the duration of the competition. Players may not change their Summoner name without permission during the competition.

Other than obvious things, such as toxicity and suspensions, there is no "required" rank in order to participate on a collegiate team. However stronger teams have a balance somewhere in the Platinum or higher area.

From what I can understand, there are no rank requirements but specific schools may have actual rank requirements to represent them at events (as I doubt certain schools would want to pay air/hotel for a bronze 5 to go to one of these things).