Captain Haddock,
Your example 「この車は赤くないのに、好きです」 is rather awkward but a viable interpretation is, "Though the car is not red, it likes (something)." Note the contrast between -noni and -ga or -kedo;
この車は赤くないが、好きだ。 kono kuruma-wa akakunai-ga, sukida.
この車は赤くないけど、好きです/好きだ。 kono kuruma-wa akakunai-kedo, sukidesu/sukida.
This car is not red, but I like it.
I take the liberty of making a tentative account for other posters to freely examine.
In my view, -noni seems to "copy" the subject of the sentence it belongs to and transfer it to the second clause as its subject. This function, however, can be overridden by an explicit subject in the second clause.
この車は赤くないのに、彼は買った。 kono-kuruma-wa akakunai-noni, kare-wa katta.
Though this car is not red, he bought it.
Here is another example of a subject implied by -noni;
私は美しいのに、だれも愛さない。 watashi-wa utsukusii-noni, daremo aisanai.
I am beautiful but love nobody.
In order to say, "Thought I am beautiful, nobody loves me," a trick is needed in the second clause in order to explicitly say that the subject there is not 私 or I;
私は美しいのに、だれも愛してくれない。 watashi-wa utsukushii-noni, daremo aishite kurenai.
Though I am beautiful, nobody loves me.
The trick here is the auxiliary verb kureru. Since it designates the speaker as the recepient of the action, the subject of the second sentence cannot be 私, which is none other than the speaker. Now that 私 is crossed out as the subject, the only remaining noun phrase だれも is allowed to be interpreted as the subject of the second clause.
The fact that -noni cannot follow -desu is another support for my position. By evidence from relative clauses, it is assumed that -desu cannot appear in subordinate clauses;
*帽子をかぶっています男の人は、彼女の父親です。
as opposed to
帽子をかぶっている男の人は、彼女の父親です。
bōshi-o kabutteiru otokonohito-wa, kanojo-no chichioya desu.
The man that is wearing a hat is her father.
If the clause marked by -noni is construed not as coordinate to the other clause but as subordinate, the implicit subject in the second clause can be assumed to be the topic of the subordinate clause.
Note
愛さない is the irregular -nai form for 愛する, which usually conjugates as a suru-verb.
Flam