Not really, but I think it's rather "a set of things" that lead to the (very) vast majority of games not supporting console mods. So "officially", no one is against, no one forbidden mods, but... for studios, providing mod support on console is simply not worth it, generally.
This is true.
I was a game tester for 9 years, and have seen the process for getting stuff on consoles many times.
The major problem is submission. Sony, Microsoft and even Nintendo have a process called submission. If you want something on the console, you have to submit it. They check that it follows their rules and a few other things, and then either allow it or deny it.
Submission is what complicates mod support on console. Everything, even patches have to go through submission and submissions cost money. It's probably changed, but when I was a tester, one of the leads on a project said that a submission was 20k$ a pop and 10-15k$ for patches/DLC for each console, which is why developers tend to make sure they pass submission.
If you've noticed mod support for Fallout and Skyrim on consoles is very curated and limited. That's because those mods had to go through submission just like everything else does. Someone paid the fee and I doubt it was the mod creators, which is why you have to pay for them on console while more, higher-quality mods are available for free for the PC version (they are also completely separate from any Bethesda control).