Yes, many places take cards. And yes, even more places take USD (a few even, oddly, only take USD). However, carrying pesos will make your life (and the lives of those who are serving you at restaurants and driving you in cabs) so much easier. Some of the best restaurants and bars on the beach are cash only, and if you're wanting to support local businesses there, show up with the currency that's easiest for them to make a transaction with. You'll save money using pesos over USD.
Tulum beach road, from start to finish, is relatively long (at least for walking), and there are cabs driving up and down the road at nearly all times of the day and night to make getting to and from your destination — especially if you've had a couple of margaritas — much easier. These cab rides are just a few pesos since they are short trips and can only use cash for these.