Obviously most writing systems are derived from older systems, so I tried to only list systems that might have independent origins (although both the Semitic and Western systems come from an area that had writing for a long time, so it is questionable). Old Persian cuneiform was left-to-right (https://en.wikipedia.org/wiki/Old_Persian_cuneiform), while the Pahlavi and modern Persian writing systems have a common origin with Hebrew and Arabic (i.e., Semitic).
Thai (at least today) is left-to-right, but anyway Thai is highly irrelevant since it is derived from Indian writing systems and probably ultimately from Semitic ones (https://en.wikipedia.org/wiki/Brahmi_script).
Thai (at least today) is left-to-right, but anyway Thai is highly irrelevant since it is derived from Indian writing systems and probably ultimately from Semitic ones (https://en.wikipedia.org/wiki/Brahmi_script).
Old Persian: left-to-right. Calendar: solar. Sumerian: left-to-right. Calendar: lunisolar. Egyptian: left-to-right. Calendar: solar. Chinese: right-to-left. Calendar: lunisolar.
So, anyway, so far the evidence is not strong at all (and I wasn't saying it is), but I'm not yet convinced there was definitely no influence.