Yes. For long exposure sell a suitable quantity of in the money puts to give you the equivalent exposure to what you wanted to buy. For short exposure, sell a suitable quantity of in the money calls. (When deep in the money, option contracts behave like stock equivalent.) You'll collect a credit the value of which will be the intrinsic value (difference between stock price and strike price) and any extrinsic which should be small if the contract is sufficiently in the money. This credit will be used if and when you buy the contract back, or if contract is possibly exercised and the underlying position assigned to your account, leaving the net P&L being the net move on the underlying. It bears repeating: Being in the money these contracts may be assigned if they're exercised by the buyers. If and when this happens you will therefore automatically buy or sell the underlying/stock (which is precisely what you want) at the option contract strike price, and it will be deposited in your portfolio as it must be due to the option contract, despite it not formally tradable. Once in your portfolio you will be allowed as normal to directly close the position as and when you choose.
Business is separate from religion. Hasidic Jews are known to have traded pork belly futures in bygone days.