Then I saw another beast rising out of the earth. It had two horns like a lamb and it spoke like a dragon. It exercises all the authority of the first beast in its presence, and makes the earth and its inhabitants worship the first beast, whose mortal wound was healed.
Revelation is one of the most difficult books of the Bible to understand. This is partly because it is symbolic, and partly because some (if not all) of its prophecies have not yet been fulfilled. We should be cautious about presenting any interpretation dogmatically.
Some interpreters identifiy the Beast of the Sea with the Papacy. This is because this Beast has ten horns, which associates it with Daniel’s fourth beast (i.e. Rome), but has crowns on its horns, which might indicate that it represents a later stage of the Roman Empire. If you see the Papacy as a direct successor of the Roman Empire then you might equate the Beast of the Sea with the Papacy.
Some interpreters identify the Beast of the Land with Islam. This is because the Beast of the Land is sometimes equated with the “false prophet” referred to elsewhere in the book (Rev 16:13). Since Christians do not accept the utterances of Mohammed as revelation from God, some may identify Mohammed as this false prophet and so identify Islam with the Beast of the Land.
However, as the questioner points out, these two interpretations cannot easily be reconciled as there is no sense in which Islam causes mankind to worship the Papacy. Therefore it is likely that either one or both of these particular interpretations is false.