Time Series Forecasting for Multiple Customers using one RNN
Here are a few rapidfire ideas:


Does the customers affect each other in any way? If that is the case, you need to feed the information of multiple customers at the same time to your RNN. If not, then I would advise creating a time series for each of your customers and feeding it separately to your RNN.
What is it you are trying to predict? Is it a percentage chance of something? Is it a number (e.g. volume of customer purchases). You need to create your outputs, and the inputs you will use to predict that output accordingly. You may also use multiple RNNs if some of your outputs have no relation to each other. For example, if you are trying to predict the volume of purchase for a customer and whether a customer will leave or not, you may want to create two seperate RNNs that will take different inputs (e.g. use the average purchase volume as input for the RNN that predicts the customer volume, and use the frequency of customer visits as input for the RNN that predicts whether the customer will leave or not
Is there huge discrepancy in values of your variables? (e.g. some customers only do 10 dollar purchases, but the others do 100,000, and you want to feed the information of both to your RNN) If that is the case, you may want to "normalize" your variables as well as the outputs (labels) you are trying to predict
Do you really need an RNN? If your customers' outputs are independent of the sequence of variables from the past, then drop the RNN and use something simpler like feedforward neural network or logistic regression
Are your customers' outputs affected by variables from a long time ago? If so, you may want to add a memory component, such as an LSTM, to your RNN
Does your customers have any periodic components? (e.g. the customer usually buys something 10 days after adding it to the shopping cart). This tells you the lookback (how many past days' data you need to feed to the RNN) you will need for your RNN


Hope it helps. I must admit however, that without getting a sense of the inputs and outputs it is difficult to answer this question.