Society in the United States is always evolving, generally trending toward equality and advancing personal freedom and liberty. Since the founding of America, we have seen great movements toward the goals and rights our constitution inspires, at times dramatic and others quiet and slow. I have noticed a current reversal of this trend based almost exclusively on religious belief being pushed onto the citizenry.
Christians find abortion to be sinful....and so fight against it in often sinister and backdoor ways, chipping away at the freedoms of others to use their lawful rights.
Christians find homosexuality to be sinful....and fight against the choice of others to love who they want, marry, and enjoy the rights given to everyone else who happen to be heterosexual.
Catholics find contraception to be sinful....and so fight against the use of it by denying those not wishing to become pregnant easy access.
Does this go against the separation clause of our Constitution...and more importantly, are these things (and many others) a roadblock to societal progress?
As to your first question, does any of the activity you've listed constitute a violation of "Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof"?
No, it clearly does not.
People are free, constitutionally, to associate with those they choose, and when people choose to associate for the purpose of creating what is in effect a PAC, to address issues such as abortion, homosexuality, and contraception, like any other special interest group, they have every constitutional right to do so, no matter what the religious or lack thereof makeup of the people in the PAC.
As to your second question, let's take a foundationally accurate look at the three issues you mentioned.
Abortion always takes the life of a prenatal human, and the right to life of those humans we do know nowadays to be alive rightly takes precedence over the right to freedom of action of another to take that life when their own life is not at stake. So
true progress is found in putting an end to such unjustified killing of humans.
As to the oxymoronic "homosexual marriage", requiring that the domestic partnership civil unions of
homarried (or appropriately relevant termed) people (same-sex partners) not be ludicrously included in the definition of
married people (a man and a woman as husband and wife) is, like not allowing the definition of dog to include cats, a mentally intelligent respect of words and their true meaning and an emotionally intelligent respect of humanity's time honored institutions and those people who partake in them. So
true progress is not allowing the mentally and emotionally regressively violational "gay/homosexual/same-sex marriage", but in preventing it, and, additionally, creating in every state a domestic partnership civil union for same-sex partners called "homarriage" or the like.
And, as to contraception, most regular "birth control pills" used today contain progestin, a synthetic hormone that functions to prevent implantation of a newly created human into the uterine wall, thus killing that human, and, in addition, all Plan B, "morning-after" pills, and the like, also function to kill the prenatal human. Thus all of these products are abortifacients, meaning they cause chemical abortions. So opposition to the indiscriminate use of these products is simply part of the opposition to the unjustified abortion of humans, a good thing with respect to human rights. The only regressive aspect of Catholic (or Muslim, or whatever) opposition to the use of non-abortifacient birth control such as condoms, diaphragms, and others, requiring that all sex never "spill seed" in any way, is that such opposition contributes to the rampant over-population of our planet at a time in our history where over-population threatens to exterminate all of humanity in more than one way, so the progressive thing to do would be to support such non-abortifacient birth control methods.
So, for the most part, with the singular exception of opposition to non-abortifacient birth control, the behavior of the people you're complaining about is good and progressive behavior itself. Thus the answer to your question about are they creating a societal roadblock to progress is for the most part "no".