I’ve heard the following sentences, unless there’s something wrong with my hearing.
There is, I’m sure a difference between these two sentences.
What do you say @NearlyNapping, @Arinker, @Anglophile, @Torsten, @Alan ?
The first time I read these I used the same emphasis on both sentences and thought they had the same meaning.
The second sentence, though, could be expressed as “I would like to think that charity begins at home [, but sometimes I have my doubts].”
I think the emphasis is important if you want to clearly say something different from the first sentence.
Thank you Arinker, you think exactly the same about the meaning of those sentences as I do. Now, that I’ve had confirmation of a native speaker, I can sleep on both ears, although that may be a little difficult. 
The difference is so subtle that in practice they will be understood to have the same meaning. With more context they could potentially have different meanings.
I like to think that charity begins at home.
To me this means “I’m optimistic that charity begins at home”.
I would like to think that charity begins at home.
To me this means "I HOPE charity begins at home.
But here’s the thing. The difference is so subtle that the above interpretations are trying to read more into it than what the speaker meant. So I am trying give it meaning where likely none exists. I think if you asked a dozen native speakers the difference, they would all do the same thing I did - and end up with different ways of saying it.
It’s like explaining the difference between violet and purple.
Bottom line is, don’t worry about it. It doesn’t matter which way you say it. It’s nothing more than a choice of words.
Thank you for your answer NN.