Would portraying a black man speaking BBC English be disrespectful? Would portraying a white women speaking Thai with a Cambodian accent be disrespectful? Would portraying a Scot with a Yorkshire accent be disrespectful? Neither Ethnicity nor localisation has a monopoly on stupidity.
Oh sorry, you meant respectful as in good!
Look at the phonetics of the language/region they are from. There are things that will always be hard for speakers to adapt provided they did not learn the language early: "p" and "b" in Arabic, "r" and "l" in Japanese. There are lots of others. Now, look at the grammar of languages: No future tense in Japanese, no pre-positions in Polish (but declinations), no neutral in French. Those things will seep into the foreign language. Those are little things but they do add up. So, using those little idiosyncratic elements will add depth to your speakers' narrative.
(Side track) Vocabulary is a great indicator as well: It is possible to get by with 500 words but however good your accent is, you will never pass as a native speaker. Even after years of studies and speaking, you still encounter words that you have no idea about...
Note that accents are dependent on where and who teaches you. I know some very white folks who speak French with an Algerian accent. I know black folks who speak Spanish with a Mexican accent.
As for accents, there are millions of them. The best way is to listen to them but it can be hard to find the right people to listen to! Going on holiday is a good indicator or hanging out in a tourist attraction close to home. Feel free to go and ask people to record them. Say it is for a book/play/project that you are collecting accents. Most people should be happy with doing it as long as you do not take too much time out of their lives.
If you live near a university with a philology department, pay them a visit and start asking questions. You will learn a lot.
Edit: I know the OP meant respectful in a racial offensive way. So, instead of using political correctness (read: New Speak), I opted to try science.