It was not an issue for me the two times I applied for a mortgage, to buy then to refi. But I did cut it very close the second time. For the refi I used Box, at the time the lowest rate in the entire USA, and they don’t care where your credit is at as long as it is 760+.
I am at 30 years/3.375 with no MI, so I don’t expect to refi my house again. By my calculation, the 30 year treasury would have to drop 0.5 below its all time low, to around 1.75%, before it would make sense for me to refi.
When I start looking for another property I will stop churning cards though.
The safe way to do it is to do all your applications for the year on the same day (called an app o rama), which is reported as a single inquiry. You also have to check online and avoid banks that look at more than one credit agency. I think capital one does this, so applying with them is 3 times worse than chase.
Inquiries from credit card apps drop off after 2 years, and don’t really have too big an impact. But if you’re really worried, you can check your score first and only proceed if you are at 790+, which provides a safe margin. I also have kept one no-fee card open for 8 years, which also helps my score.