So your question is whether or not a Christian or LGBT owned business would receive special treatment or privilege as a result of being owned by a Christian or LGBT person? With respect to government contracts or otherwise? I think the answer is almost certainly not in most cases, but the answer is more complex than that and a complete answer should explore interactions with both government and society.
If we are talking about the government. Then a Christian-owned or LGBT-owned business like a bookstore or restaurant or building contractor should be treated exactly equally by the government. The 1st Amendment declares that Congress should pass no law respecting an establishment of religion and the 14th Amendment states that no person shall be denied equal protection of the law. This should be true when it comes to taxes, building permits, inspections, licensing, grant programs like Covid PPP business loans, and yes, contracts. To the extent that one type of business owner is being advantaged or disadvantaged due to their identity, it is most likely the result of some government employee illegally tilting the balance in favor of one or the other and basically abusing the authority that we the people have granted them. These people are breaking the law and should be fired, whether or not they are tilting the playing field in favor or against Christians or against LGBT people. Are there examples of specific government entities that tilt the playing field one way or the other? Perhaps. It is a big country and I'm not aware of what every single city or county across the country is doing. I expect there are some examples were Christian-owned businesses are advantage and some where LGBT-owned businesses are advantaged. In my opinion, neither should be the case. But in both cases we are talking about a vanishingly small microscopic fraction of the total business conducted by both Christian-owned and LGBT-owned businesses. In other words it is trivial and mostly performative either way.
If we are talking about wider society. Are there examples where Christian-owned or LGBT-owned businesses are afforded advantages or privileges, or disadvantaged due to the identity of the owner? Of course. When we are talking about things like bank loan officers reviewing business plans, landlords reviewing rental applications, employees seeking employment, businesses seeking business relationships with other businesses as suppliers or customers or partners, and so forth. Then there is going to be a lot of discretion and discrimination because people bring their own prejudices and biases into their business relationships and interactions. In some parts of the country I would expect Christian-owned businesses to have a tremendous advantage (or privilege) over LGBT-owned businesses. In other parts of the country it is likely the reverse. On balance, or on average, across the entire country, I would expect that being a Christian-owned business still confers more advantage or privilege compared to being an LGBT-owned business. Even here in the greater Portland metro are which is pretty liberal and LGBT friendly I see a lot more incidents on the news about LGBG-owned or LGBT-friendly businesses being vandalized and attacked than Christian-owned businesses. This was 2 days ago near my house, for example: https://www.yahoo.com/lifestyle/vandals ... 00859.html