if you read a book from another culture, or even an older time period, and it influences you, is it part of your culture?
In everyday use, the term “culture” usually connotes thought patterns and behavioral tendencies that are widely shared within a community, and they may be unique to a particular time and place. The definitions I have been proposing do not included this connotation.
For now, I am willing to stick to the simple definition of culture as socially communicated thought patterns and behavioral tendencies. I would remark that these patterns are almost always shared within a community, because most communication takes place within a community. When you are influenced by a source outside of your usual community, you are going to be a bit of an oddball, unless you can convince your close associates to adopt the novel influence.
I would add that an interesting issue within a community is the kind of alternatives and alien influences that people are willing to tolerate among other members. I do not think that “tolerance” is a purely scalar variable, with some communities having more and some having less. Rather, I think that tolerance is multidimensional, with some communities more tolerant along some dimensions and less tolerant along others. So if in 1950 the typical American could tolerate the N-word but not the F-word, and today it is the reverse, that fact does not tell us that people today are more or less tolerant along some non-existent scale.
Some aspects of “culture” may strain the definition of “community”
For example, in the US, we drive on the right hand side of the road, stop on red and go on green.
Not every place in the world works that way.
But those rules are very wide spread, it’s kind of a stretch to say they are part of some community. (Maybe “community” can be much larger than I am thinking.)
But they (and many other rules like them, some in law, some not) are very much part of our “culture.”