Moshe S: There is currently one Shul in the country that identifies as Orthodox with a woman Rabbi (and their website explicitly calls them “Open Orthodox”). As far as I know, they don’t have a microphone. Even if they did, though, the RCA already said (3 times) that they’re not Orthodox.
Joseph: If I call myself Chinese and then shoot someone and claim that it’s okay because I’m Chinese, does that make all Chinese people murderers/condoners thereof? Of course not. I don’t care if someone calls themselves “Modern Orthodox” and uses that to mean “Orthodox Lite”. They’re wrong. And them being wrong doesn’t make those actually Frum people who also call themselves “Modern Orthodox” less Frum.
There are two microphone systems that some claim can be used on Shabbos. One is for sure Muttar as it doesn’t involve anything at all. It actually just uses well-placed water systems to amplify sound. There should be nothing wrong with that. The other uses a Grama and isn’t really used by any Orthodox Shul (but is used in some Orthodox old age homes, last I heard).