I think we are already compromising in ways that both protect religious freedom and persecuted groups and that there is room for continued compromise in the future.
Personally, I think the definition of a religious organization is too loosely defined. I would categorize an organization as religious in nature if they
A) Hired only people of the same faith
B) Provided services to only people of the same faith (excluding services that are free)
C) Performed functions that were inline with well defined religious beliefs.
That being said, I can accept compromise. I can accept the more loose definition of any non-profit that is privately funded and follows a set of religious principles be eligible for exemption as a religious organization. I can also accept the compromise that tax-exemption be interpreted not as a form of public funding.
I draw the line at exemptions allowed for for-profit companies and non-profits operating with public funds. The harm done to the groups which are targeted for discrimination greatly outweighs the meager additional protections for-profit and publicly funded non-profits gain.