There is nothing to suggest that the Shah put an end to secular democracy which was seeking to modernise the country as it became a secular dictatorship which also sought to modernise the country. It put an end to a secular democracy. Basically the US tried to correct something which did not exist and ended up with what it had hoped would not come about.
That's like saying if some foreign power came to the US removed the president with force then installed an un-elected kind dictator as head of state in his place, and the dictator re-established the trappings of democracy according to his whims, that would equate to no change in US democracy.
The US and Britain destroyed Iranian secular democracy and we ended up with a religious state as a result.
And they did it for one reason, greed.
That is what drives both nations. To understand their actions you must understand it is unmitigated apish greed behind all of it.