What are the cons of Separation of Church and State?

Answer 1

One is that this country was founded on the religion of god....

Actually, while the vast majority of the Founding Fathers were very religious or spiritual, the nation itself was NOT founded on any real religion. Rather, it was founded with inspiration of a general non-specific Deity. Certainly, most of the Founders' faith was grounded in Judeo-Christian beliefs, but the USA was NOT founded specifically on any religion's beliefs, including on any specific idea of what God (or the Deity) was or was not.

Back to the original question: perhaps the major con of not having a formal State religion is a loss of homogeneity. By having a single religion (and, realistically, legal discrimination in favor of that religion), the country is assured a very common basis of beliefs and foundation of identity. Heterogeneous societies do not have this common foundation - which may or may not make forming a functioning society more difficult.

Overall, the historical experience of the past three centuries (not just in the USA, but in other countries as well) has generally shown that there are no (or negligible) practical consequences of having Separation of Church and State. That is, there are no real cons.