Are non-citizen Muslim professors and students going to be removed from US universities and subsequently deported by Trump's ban?

The current ban applies only to people who are outside the US. Nobody knows what Trump might do in the future, though.

Edit: The situation keeps changing, and I will not be updating this answer. Stack Exchange is not a news service.

I know that some have the "alien of extraordinary ability" work visa, but what about for others that don't have such status?

Even green card holders are impacted by the ban. As far as I know, only diplomatic visa holders are not impacted by the ban.

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A message that I received from my university on 2017-01-29 at 6 PM UTC seems to indicate that in Massachusetts the ban is lifted for the next seven days:

Early this morning, the Massachusetts federal district court issued a temporary order that restrains the government from enforcing the Executive Order to detain or remove holders of a valid visa or green card who travel from the seven countries to the US through Logan Airport. This order is in effect for the next 7 days. The seven affected countries are: Iran, Iraq, Libya, Somalia, Sudan, Syria, and Yemen. […] We encourage you to fly back to Boston--directly to Logan Airport--as as soon as possible, and before February 4.

An update from my university I received on 2017-02-02 at 9 PM UTC:

Suspension/Cancellation of Visa Appointments at US Consulates Abroad, Revocation of Visas, and Suspension of Adjudications at USCIS

Dear International Scholars,

This is to confirm that the US Department of State has issued guidance to consulates worldwide directing them to cancel visa appointments and suspend visa issuance to nationals of Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen until further notice.

This means new scholars who were born in or who are citizens of these seven countries will be unable to get their initial visas to enter the US and current scholars traveling home or to conferences will not be able to renew their US entry visa stamps until further notice. Department of State is also cancelling green card interviews and suspending the issuance of immigrant visas at consular posts.

In addition, the US Department of State issued an order revoking all currently valid non-immigrant and immigrant visas issued to nationals of these countries.

You may read the announcements on the Department of State website at https://travel.state.gov/content/visas/en/news.htmland at http://www.politico.com/f/?id=00000159-f6bd-d173-a959-ffff671a0001.

Links to articles describing the situation in more detail can be found at http://www.wbur.org/news/2017/02/01/visas-revoked-state-departmentand https://www.pri.org/stories/2017-01-29/these-are-new-instructions-state-department-rushed-embassies-worldwide.

If you are currently in the US and are from one of the countries listed above, we continue to recommend that you DO NOT travel outside the country at this time. If you absolutely must travel, please be aware that you risk not being able to return as planned.

If you are outside of the US and have not yet contacted the ISchO, please e-mail us as soon as possible.

You may also be aware that in addition to visa issuance and entry into the US, the recent Executive Order refers in places to the “adjudication of other immigration benefits.” It is our understanding that in addition to suspending visa processing and entry into the US for citizens of Iran, Iraq, Libya, Somalia, Sudan, Syria, and Yemen, USCIS has also halted adjudication of applications/petitions (including F-1 OPT, other applications to change or extend nonimmigrant status, and permanent residence applications) for citizens of these countries. However, at this time, it appears that USCIS is still accepting applications/petitions – just not making a final decision.

We will continue to provide updates as more information becomes available.

Sincerely,

Academics are certainly being barred from entry at this time. Several examples are in the New York Daily News article linked below (date: Jan-29, 2017). For example:

An Iranian doctoral student at the City University of New York, Saira Rafiee, was stopped in Abu Dhabi and not allowed to board a U.S.-bound flight, political science Prof. Kenneth Paul Erickson wrote. Rafiee had traveled to Iran for the winter break.

Ironically, Saira wrote this morning (quoted in PSC-CUNY email): "As a student of sociology and political science, I have devoted a major part of my scholarly life to the study of authoritarianism..."

Edit: Some relevant news links:

• USA Today counts 23,763 international students as being affected by the ban (using data from the Department of Homeland Security).
• Yahoo Finance reports that the Association of American Universities released a statement saying, "The order is stranding students who have been approved to study here and are trying to get back to campus, and threatens to disrupt the education and research of many others."
• CBS News reports on individual responses from the presidents of several top universities.
• New York Daily News reports on experiences of several students caught in the ban at JFK (including Saira Rafiee, above).
• PSC-CUNY released the full email statement that I referenced above.