As a separate order, membership in the AMORC is a separate decision.
I suggest an answer to the opposite question - Should Masons avoid joining AMORC? To me the answer is no. There's no conflict that I know of when it comes to what outsiders can learn of the AMORC lessons. The AMORC is a lot smaller than Masonry but there are percentage of AMORC members who are brothers. Some Masons have decided to become AMORC members and are happy with their membership. But the focus of their lessons seems to be different enough that some Masons would not want to join for reasons not directly related to Masonry.
But the positive question - Should Masons consider joining the AMORC? There's a lot to Masonry that is not related to Rosicrucian topics so I don't think it's automatic that a brother would want to consider it. There are reasons one individual might not want to join, as with nfasson's objection to New Age ideas that appear core to AMORC (from my perspective as a non-member who has read some of their books). There are reasons one individual might want to join, if Rosicrucian topics keep coming up in your life.
In San Antonio there is an AMORC group that hosts monthly open events. I've been to a few of them but for the moment I have not decided to join. I'm too busy with family, work, lodge and church activities to fit in another fraternal order. It's the same line of reasoning why I have no joined an American Legion lodge as well. I know what happens when I join a new order - my signature does list the 3 years I've been in the east.