Up until this, charging money for mods has been illegal because of licensing reasons. So (nearly) everyone who mods does it because they like to mod. The worry is now people are going to mod because they can get money that way and the effect those people could have on the modding community.
The other thing is that because the modding community knows that no one is going to be making modding off of money, mod authors are pretty nice about other modders using the stuff they've come up with so long as every gives credit where it's due. The worry now is that people are going to be making money off things that they didn't make or making needed programs and assets for modding behind a paywall. This has already caused several mod authors over at Skyrim Nexus (practically the internet home of Skyrim modding) to specify that they do not want people using their assets in paid mods in their licensing section. And some mods, like SKSE (Skrim Script Extender) are probably in the majority of mods on people's load lists.
Probably the biggest issue people have with it is how the people really profiting from all this is Valve and Bethesda, not the mod author. Currently Valve and Betesda get 75% of all the money made from mod sales, and the author only gets 25% and that's only if their mods make over $100 a month. Yeah... a lot of people who would be okay paying for certain mods aren't willing to pay Valve and Bethesda for it. Especially as most of the "core" mods people instal are mods designed to fix all the bugs that Bethesda got around to fixing, or to get rid of the "casual gamer" balance TES has evolved into over the years. So no one wants to "reward" the gaming companies who made the vanilla games instead of the people who are actually fixing the games (or doing the bulk of the work to make awesome DLC for them).
Linked to that is the precedent paid modding leads to. The big worry is that if game companies find out they can make money off of modding they will make free modding much harder to do. Mostly by making it impossible to get the game editor without going through the company as well as making it difficult to upload game altering content anywhere but to the company approved modding site where people will have to pay to play game mods (with most of the money going to the game developer, not the mod developer). The reason this is a worry is because Fallout 4 is right around the corner and modders are wondering what the licensing is going to be on that. Because pretty much, all (legal) modding is constrained by whatever licensing is put in the game, and nobody can do anything about it. In short, modders are wondering if game companies are going to be offloading a lot of bugfixing and DLC content creation on them, only for the game companies to get most of the money from people buying the content. This is especially true for people who use over 100 mods in their load order. Not only are they worrying that their going to be paying $60+ for the official game and DLC, but even if they only have to pay a dollar per mod, that makes their mods cost more then the official game and the game company gets most of it. (Yes, people are already talking about mod piracy.)
Probably the people having it the worst right now are the mod authors who are now charging money for their mods and have taken them off the current modding websites. Let's just say it's gotten pretty nasty for some of them.
For rather obvious reasons, Valve and Bethesda are coming under huge amounts of fire for this. I'm actually not all that mad at Valve. We've got the Steam Trading Market and the Workshop tab. Exactly how long did we think it would go before they thought to combine the two? It'll be interesting to see how this works out with games other then Skyrim, though...
Bethesda though has been a poster child for everything good about game modding. Up until this point, they've let people get the game editor for free and have let people do whatever they want with it so long as the people using their assets don't make money off it. Now though, they're directly profiting from people's mods, and profiting better from it then the actual mod authors are. The big worry is that they'll want this from future games by default. And while people are plenty willing to pay Bethesda for the base game and DLC, they don't want to pay them for work they didn't do, (or in some cases, pay them for not doing enough bug fixing that they are now having to pay more money for to fix).
I'm still kinda wondering why they picked Skyrim for the game to introduce this concept. TES modding has been around since Morrowind and the TES modding community has had a good 15 years to estabish it's own way of doing things, with no one official butting into it. While launching this concept with Skyrim will definitely let everyone know about it, it's also the best way to stir controversy, mostly of the negative sort. Skyrim came out in 2011 and the modding community has been going strong since 2012, when the Creation Kit and the last DLC were introduced. Everybody knew how the modding system worked. Messing with a modding community that big means that everyone who's even a tiny bit into modding is going to know exactly how paid modding is going to work under Valve/Bethesda and there's no way for Valve to slowly introduce it into the community and let people get used to it. A lot less negative controversy would most likely have happened with a different game at the expense of not as many people paying attention to it at launch.
As off now, there's a huge split in the Skyrim modding community between the mod authors who are endorsing paid modding on one side, and most mod users and the mod authors who have said they will always have a free version of their mods available on the other. Easing this split is going to take a lot of work, and Valve and Bethesda have lost a lot of good will from mod users. Making that good will up again is going to take a lot of time.