This sentence is a proper use of would rather. And it contains an infinitive.
Would rather is an idiomatic predicate that means prefer, and has many of the same syntactic affordances and restrictions as prefer, although would rather doesn't use the infinitive complementizer to, while prefer requires it. Both are negative triggers and can trigger NPIs, for instance,
- I would rather do anything else.
- I prefer to do anything else.
In addition, both predicates can take a that-clause complement with an untensed verb:
The sentence in question is simply an untensed (i.e, infinitive) verb form in such a complement clause, with the that complementizer deleted:
- I would rather (that) [the walls remain painted in a neutral tint].
Note that if you use a form of be instead of remain, you get the infinitive form be:
- I would rather (that) [the walls be painted in a neutral tint].
- *I would rather (that) [the walls are painted in a neutral tint].
There are a lot more infinitives around than one might suspect from Miss Fidditch's class.