Is it safe to use user defined variables inside stored procedures in MySQL?

Currently I'm working with Stored Procedures in MySQL and I'm using in some procedures **user-defined variables** and I've seen that type of variables are initialized in the current session and keep their value until the session ends. I was also working with statements like select into @user_defined_variable but I realized that doing that is very risky, specially on logins/authentications. So the solution in this case was to use the statement set @user_defined_variable instead of select into. But I'm really not sure if it's enough using the set, because that type of variables will keep their value while the session is not finished. Now imagine that the server receives several requests at same time on the Stored Procedures that are using the same @user_defined_variable, can exist a collision of values in this case? For example, if the stored procedure called login uses the user defined variables @uuidUser and the stored procedure called home also uses the @uuidUser, does exist the risk that the home procedure uses the value of @uuidUser assigned inside the login procedure? **Note**: I'm working with Node.js and I only have one connection to the MySQL instance,I don't create a connection for every request. So the @user_defined_variables will always exist.