If I have a party of characters who do not really approve of the good guy, do I have to skip quests like A Village Under Siege if I want to keep a high approval of Morrigan?
In general, no. Almost every quest can be done in more than one way, with your choices having an impact on several things, including how your companions react. In most situations, it is possible to avoid the loss of approval on a specific companion or two, at a cost of some others.
As an example, reading through the page you linked for A Village Under Siege, there are only three mentions of Morrigan on the whole page. Two options for disapproval, both of which seem to be avoidable, and one option for a +2 approval, though at a cost of -5 to Leliana.
Part of the key to this, is remembering that the members of your party aren't evil; if they were, they'd be out there helping the darkspawn. In Morrigan's case, she's a bit self-centered and overly pragmatic, and will tend to look down on you jumping in to save the day like a shining white knight, or especially agreeing to something time consuming like helping a man find his daughter so he will help you, when you could just coerce him into it. Taking a more direct route will usually work.
All of that having been said, however, I do not personally know the entire game inside and out, so there may still be some situations where it is downright impossible to avoid displeasing certain party members, or else doing so would require an option you're just not willing to take. My advice if you encounter one is simple; don't sweat it.
Between dialogue choices, personal quests, and of course, gifts, approval is easy enough to come by if you're at all trying, so you should still hit 100 in no time. The bonuses for high approval hit their maximum at 90, so once you're at the top, you can lose up to ten at once before anything at all changes. And losses of more than ten approval in one go are quite rare, usually only happening as a result of deliberate insults during a companion's personal quests, romance dialogue, etc. Focus on making your active companions happy most of the time, and you'll generally do alright.