Is there any particular reason the Russians were so open to female rule, even that of foreigners?
No, there was not.
In 18th century that was out of desperation - the male line was extinct, so the women had to take matters in their hands.
Even Sophia's regency can be viewed like this...
Ye, I think it was a game of chance. A coincidence.
The first woman in the Romanovs dynasty to take power officially, Sophia happened to be quite a capable leader. Well, she was not too successful, but she was definitely no worse than any male ruler. The Russians saw it, remembered it, she kind of started the trend.
After her it went easier for a female on the throne, there was already a precedent.
When there was no longer any problems with male line any significance of tsarinas disappeared - after Alexander I there was a steady male line.
So women on the throne was a temporary dynastic problem with male line of the Romanovs.
... the Tsars have always been the head of the Church ...
Nope.
Not always.
Only after Peter the Great.
By the way it was widely believed that medieval French kings could cure people of measles or something. Not sure about British kings though.
The Russians tsars could not do anything like that, they were not expected to do any such things.
But there were a lot of revered Orthodox saint people all over the Russian Empire who were believed to cure people. I mean you overestimate the religious spiritual aspect of tsardom. First and foremost the tsars were earthly rulers.