Of interest: the order covers sexual orientation and gender identity, and it does not include an express exception/exemption for religious-based objections (something of a hot topic in the wake of Hobby Lobby).
However, the new executive order is merely amending prior executive orders (mostly just adding sexual orientation and gender identity to the list of protected classes). You can read the existing executive order regarding federal employment here (#11478). And, you can read the Executive Order 11246 regarding federal contractors here. Notably, the latter already includes a religious exception:
Section 202 of this Order shall not apply to a Government contractor or subcontractor that is a religious corporation, association, educational institution, or society, with respect to the employment of individuals of a particular religion to perform work connected with the carrying on by such corporation, association, educational institution, or society of its activities. Such contractors and subcontractors are not exempted or excused from complying with the other requirements contained in this Order.I'm not sure what took President Obama so long - this order was announced over a month ago. Sometimes we get further explanations of the executive orders in a presidential memorandum - but I don't see anything on the Presidential Memoranda website (yet at least).