There are two senses of should. One is "If you want A, then you should do B", meaning that B makes A more likely. The other sense is that of duty, of having a moral debt that one is obligated to pay.
When morality is treated as a duty, what one "should" do, it is an imposed burden, and some people don't like to be imposed on. Moreover, these people will look for ways to evade that burden.
When, instead, they say "I can act according to my moral preferences", they are picturing the satisfaction of acting according to their own preferences, similar to "I can eat according to my taste preferences".
It's the alienation of values into the imposed will of external and sacred authorities that causes the problem for some. Some people don't wish to be slaves. They're probably in the minority. For those who like being subject to an authority to whom they owe obedience, alienation of values to an external authority probably helps them achieve the values imposed by the authority.
I think the two senses are really the same: if you accept consequentialist ethics, then the moral debt meaning can be translated as "If you want utility for person/group X, you should do B".
Whenever people use this word "should" in a sneaky way in a debate, I always find myself reminding them that it only has meaning with respect to someone or some group's preferences, and by glossing over exactly who's preferences we're talking about, people can get away with making bad arguments.
Here is an interesting exercise. Whenever, you have a 'should' statement, see if you can change it to a 'can' statement, and notice being more empowered. Examples:
Not, I should be grateful. Instead, I can be grateful! [To clarify, I mean that being grateful is something that will make you feel good. As an analogy, if you have tasty cookies lying around the house, you will say to yourself: "well, I can certainly get cookie."]
Not, I should leave a generous tip. Instead, I can leave a generous tip! [As in, you can leave a generous tip and feel good about it.]
Not, I should donate to charity. Instead, I can donate to charity!
Not, I should loosen-up sometimes. Instead, I can loosen-up sometimes!
Not, I should keep in touch with old friends. Instead, I can keep in touch with old friends!
Not, I should learn to program. Instead, I can learn to program!
Not, I should eat healthy. Instead, I can eat healthy!
The general pattern here is that, instead of making the activity a moral duty, you can make it something fulfilling which you choose to do because of its benefits.
For 'should not' statements you can substitute: 'I choose not to.' One example (you can make up more):
Not, I should not eat refined sugar. Instead, I choose not to eat refined sugar.
I'm sure that this procedure doesn't always work and you can generate counterexamples. I have not done them here. Please share your examples (counterexamples).