The title pretty much says it all, but.
When mantling you cannot switch weapons while in mantle.
Kinda a bummer that I think should be possible, especially if you need to switch to your shotgun.
Also, while mantling: you have both hands on the mantle.
Thus physically, you should be able to pull which weapon you want out after the mantle.
Thus Logically its possible and should be implemented 
When you mantle with your build out, it switches to pickaxe/(weapon/item) after the mantle.
This is a bummer while building because you cannot continue building, and have to switch back to build mode if you wish to continue building.
This definitely needs to be updated, because as I am building for example and then mantle or accidentally mantle, it switches me to my pickaxe/(weapon/item). Especially is kinda a bummer because I have to switch back to build mode to continue building.
Thus, while in build mode, if mantle, then switch back to/stay in build mode to be able to continue building.
Thank you for reading
PS: Is it a glitch or is this intended? Idk, but I think a glitch so I posted also under the respective category from my perspective as well. =