Rambam (Hil. Edus 11:4) writes (translation from here):
...base people are disqualified as witnesses by Rabbinic decree. This refers to people who walk through the marketplace eating in the presence of everyone... and the like. The rationale is that they are not concerned with their own shame.
This is cited as the halachah, in practically identical wording, in Shulchan Aruch, Choshen Mishpat 34:18.
Does this also apply to chewing gum or the like?