this is a serious problem.
I don’t think that you can deinstall Webview without damaging your System, it is to integral for Android.
But you can reduce the risk. I think the biggest danger is a some sort of “dive by attack”. I mean you are just surfing at some site witch is using the bugs to attack your phone.
So first step to reduce this risk is “don’t use the default Browser” (that one with the blue globe icon). Download FireFox, Opera or some other Browser and use that.
The second step should be (just possible because you have a rooted Phone) to disallow the default Browser to access the Internet. You can use AFWall+ (easy way) or the XPrivacy Module (more complex) to do this.
Step 3 can be to disallow apps you won’t trust to use the “show in browser” function. You can do this by XPrivacy, too. This Function is in most cases used to show Adds or the “What is new…” and “Help” texts of an app.
Maybe other users can suggest more ways to manage that this module wont be used (often) on your phone but I think these are some effective first steps.