*deep breath* Morals and ethics are technically two different things. Long story short: morals are more or less decided by the community and your background. Thus if you were raised in a community where pre-martial sex is wrong, your morals include pre-marital sex as wrong. Yet, if you from a personal stance decide that pre-martial sex is right and have pre-martial sex, you are making an ethical choice. This would make your choice immoral but ethical.
So yes, you can be moral but unethical; moral and ethical; immoral and unethical; or immoral but ethical.
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