...take a serious view of/against motorists...

You should use "of." One can have a view of something without necessarily being against it. Against means in opposition to, or in anticipation of and preparation for an event or an action. To take a view simply means to be aware of. Against is not wrong, it is simply awkward and ambiguous. The police might, may very well take action based on their awareness, but taking a view does not imply that. This is not a case of a distinction between American and British usage.

Because it's a "a view" - use of.

Here's an example of when you might use "against."

The traffic police take serious action against motorists who commit traffic offences that endanger the safety of other road users.

Sentence is corrupted.
'with'.
'view, with motorists'