How prominent is the gene-centric view of evolution among professional researchers?
What do you mean by gene-centric view of evolution

I am not totally sure you know what really means the gene centric view of evolution. Everybody agrees that selection (also) acts on genes and that selfish genetic elements exist. I think that what one calls the gene centric view of evolution is nothing but the modern synthesis of evolution (following the work of Ronald Fisher, Sewall Wright and some others such as Motoo Kimura).

Or maybe by gene centric view you refer to the concept of level of selection.

Some people however argue that because of the gene centric view of evolution, we tend to underestimate the importance of some parameters in evolution and some are willing to rename the evolution theory into Extended Evolution Theory according to new insights about how parameters such as developmental bias for example influence the evolution of populations.

Modern snythesis of evolution theory

You will find more information in this recent article that you may appreciate reading if it is not too complicated. I personally endorse the "No, all is well" opinion. It is important to understand that those who criticize the gene centric view in this article are NOT saying that selection do not act on genes neither that selfish genetic elements do not exist (thinks that R. Dawkins talk about in his books). They totally agree with those things. They just argue that the fisherian view of evolution in not enough and that according to recent findings we may want to rename our theory. The "no, all is well" opinion totally agrees with the importance of these new insights that do not come from what one may call the gene-centric view of evolution but they just don't think it is worth renaming the theory for that because our knowledge in evolution is just growing as it has always been growing and it doesn't seem that we are currently living a revolution in our understanding of evolution. I think that the main revolutions that happen to occur in evolution these days mostly have to do with the methodology of testing rather than with the theory itself. These revolutions have to do with increased computer power, better statistical methods and faster and cheaper sequencing.

Level of selection

Now, by gene-centric view of evolution you may refer to the concept of level of selection. To my knowledge everybody agree that selection occurs at different levels. Again, NOT everybody agree on the relative importance of selection acting at different level. The vast majority of research focus at evolution at the gene level, sometimes implicitly only.

To conclude, we all agree on the theoretical principles (I think) but not everybody agree on the relative importance of the different mechanisms. In saying this, I don't mean that everybody agree with everything that is written in R. Dawkins books!