I have been taking thyroxine and using various forms of HRT for 21 years now.
I always take the thyroxine in the morning about 30 mins before breakfast, with water. My reasoning, apart from being instructed to do so, is that water and an empty stomach enable it to get round the system and be digested and absorbed by the body easier.
As I have been on HRT patches and now on local application Vagifem, which allegedly does not get in the system, timing has never been an issue.
Although I have read reports that there may be a link between the two medications and potential adverse combinations, I have never experienced any problem whatsoever in using both.
For me, it has all been a very straightforward experience.