Are Muslims Exempt from 'ObamaCare' Health Insurance Mandate?And why are Christians not?

Are Muslims "specifically exempted from the government mandate to purchase insurance, and also from the penalty tax for being uninsured,"?

No. This is a fictitious claim. There is no provision specifically exempting Muslims from mandated health insurance in the Patient Protection and Affordable Care Act of 2010.
Neither the word "Muslim" nor the word "Islam" appears anywhere in the legislation (nor, in answer to those who keep asking, does the word "Dhimmitude").

Are any religious groups exempted from the mandate?

Yes. A paragraph on page 107 of the legislation provides for individual religious exemptions, though the language is non-specific with regard to particular faiths. Read carefully:

(5) EXEMPTIONS FROM INDIVIDUAL RESPONSIBILITY REQUIREMENTS.—In the case of an individual who is seeking an exemption certificate under section 1311(d)(4)(H) from any requirement or penalty imposed by section 5000A, the following information [is required]:(A) In the case of an individual seeking exemption based on the individual's status as a member of an exempt religious sect or division, as a member of a health care sharing ministry, as an Indian, or as an individual eligible for a hardship exemption, such information as the Secretary shall prescribe.

Similarly, page 128 states:

"(A) RELIGIOUS CONSCIENCE EXEMPTION.—Such term [i.e., "applicable individual"] shall not include any individual for any month if such individual has in effect an exemption under section 1311(d)(4)(H) of the Patient Protection and Affordable Care Act which certifies that such individual is a member of a recognized religious sect or division thereof described in section 1402(g)(1) and an adherent of established tenets or teachings of such sect or division as described in such section.

The above passage amends the Internal Revenue Code of 1986, of which Section 1402(g)(1) defines "a member of a recognized religious sect or division thereof" as follows:

(1) Exemption
Any individual may file an application (in such form and manner, and with such official, as may be prescribed by regulations under this chapter) for an exemption from the tax imposed by this chapter if he is a member of a recognized religious sect or division thereof and is an adherent of established tenets or teachings of such sect or division by reason of which he is conscientiously opposed to acceptance of the benefits of any private or public insurance which makes payments in the event of death, disability, old-age, or retirement or makes payments toward the cost of, or provides services for, medical care (including the benefits of any insurance system established by the Social Security Act). Such exemption may be granted only if the application contains or is accompanied by—(A) such evidence of such individual’s membership in, and adherence to the tenets or teachings of, the sect or division thereof as the Secretary may require for purposes of determining such individual’s compliance with the preceding sentence, and
(B) his waiver of all benefits and other payments under titles II and XVIII of the Social Security Act on the basis of his wages and self-employment income as well as all such benefits and other payments to him on the basis of the wages and self-employment income of any other person,
and only if the Commissioner of Social Security finds that—
(C) such sect or division thereof has the established tenets or teachings referred to in the preceding sentence,
(D) it is the practice, and has been for a period of time which he deems to be substantial, for members of such sect or division thereof to make provision for their dependent members which in his judgment is reasonable in view of their general level of living, and
(E) such sect or division thereof has been in existence at all times since December 31, 1950. As you can see if you waded through the legalese, the law sets the eligibility bar for religious exemptions quite high. According to a 2009 report on MSNBC.com, this language was originally meant to apply mainly to one religious group, the Old Order Amish, whose beliefs prohibit them from participating in public or commercial insurance. Members participate in a form of self-insurance per the language above requiring exempted sects "to make provision for their dependent members."

Is it conceivable that strictly observant Muslims might be granted individual religious exemptions?

I'm no legal expert, but I'll venture to say that sure, it's conceivable — provided such applicants are able to meet all the strict conditions set out above. It may be awhile before we know how that actually pans out, however, given that the provision mandating health insurance doesn't go into effect until 2014.
At least two sources I'm aware of, FactCheck.org and WorldNetDaily.com, have concluded it's unlikely that Muslims will be eligible for exemption.

“If the government can tolerate a religious exemption, then it must do so evenhandedly among religious believers with the same beliefs. This is sheer favoritism for a certain class of religions, or even for one religion,” wrote Marci A. Hamilton>, a professor and lawyer at Yeshiva University’s Benjamin N. Cardozo School of Law in New York.

It is highly unlikely though that HHS Secretary Kathleen Sebelius will grant equal permission to members of Christian and Jewish sects who will also face a serious moral dilemma when they are forced to purchase health insurance from providers that pay for abortions under the pretext of providing preventive care.

ObamaCare’s religious conscience exemption clause embodies the change Brother O’s Bread and Circuses regime brings to the new America. While Brother O considers all religious groups equal, being nuanced, he recognizes that some groups are more equal than others.

Hmmmm........So why are Christians forced to participate?Wouldn't that be against the Constitution?Read the full post here.More here.