Is it Mutar to have a bbq and invite friends over on July 4th, or is it chukat goyim?
It is a problem if the reason you are making the bbq is to celebrate July 4th.
What about thanks giving?
Same.
Does it make a difference if it is something that you are doing for work such as if you represent the United States or some American Association ?
Not sure what you mean, but if the reason your are making this event/party/bbq is in celebration of July 4th, it would be a problem.
Clearly I am not as well versed in Torah and it’s commentary as many of you. Why would celebrating a National, non-denominational holiday conflict with Judaism’s teachings?
There are many other halachos that apply with regards to celebrations other than Jewish holidays.
For example, ובחקתיהם לא תלכו We don’t celebrate non-Jewish holidays with the rest of the nation or world.