Are strongly homologous proteins identical in function?

I have my assumptions, but the question isn’t really clear unless we have an idea of what it is you think that it’s supposed to mean… I don’t see how being a skeptical agnostic is connected with the discussion of proteins.

I can only assume that the elephant in the room with regards to this question are creationist arguments regarding irreducible complexity.

So I’ll just jump the gun and just state that although biologists cannot go back in time, and due to the shear diversity of life and all its processes, neither can we normally provide precise details regarding how a given biological entity evolved. What biologists can do is compare the weight of evidence for competing hypotheses.

In this case, there is no evidence to suggest that the bacterial flagellum is irreducibly complex, whereas there is abundant evidence for intermediate forms of related and unrelated flagella like structures among organisms of close and distant common ancestry.

Simple discussion here.
http://www.newscientist.com/article/dn13663-evolution-myths-the-bacterial-flagellum-is-irreducibly-complex.html

More indepth here.
http://www.talkorigins.org/indexcc/CB/CB200_1.html

Further depth here
http://onlinelibrary.wiley.com/doi/10.1110/ps.051958806/abstract

and a nice paper in nature
http://www.nature.com/nrmicro/journal/v4/n10/full/nrmicro1493.html

With regards to your friends comments..“it didn’t necessarily mean anything”, does not itself – necessarily mean anything – at least to anyone who wasn’t privy to the actual conversation….in other words you need to provide more context for anyone to really know what he/she was referring to.

There is wide variety in protein structure and function. There are examples of proteins that have the same structure and the same function, different functions, reduced functions and no known functions. Hemoglobins are an example of strongly homologous proteins with differing functions.

To answer the question of does this mean anything… yes it means something. It means, among other things, that those proteins probably developed from a single copy of that gene which then reproduced itself. Alternately it could mean that the same gene is capable of making different versions of one protein.