I’ve already said not to sweat “due to” and “because of,” and here’s another pair that includes “because” that you don’t need to sweat. “Since” has been used with a causal meaning for centuries, and there’s no reason to prohibit that sense of “since,” even though some people insist we should (and discussions about it can get a little heated).
The reason for this insistence is that “since” might be ambiguous, since it can have either a time sense or a causal sense. But there are only a few instances where “since” may truly be ambiguous (“Since you came over, I feel better” — does “since” here mean “because” or “from the time that”?); in fact, most sentences containing “since” have enough context to make the meaning clear.
Bottom line: If you think a sentence containing “since” might be misunderstood or cause a reader to stumble, recast it to ensure clarity. Otherwise, use “since” to mean “because” wherever you like.