Even if it is not in your plans it should still be considered. Home equity can be a substantial portion of net worth. Not considering it will give a distorted picture of where you stand.
The title of this thread is "Do you include the value of your home when calculating when you will reach FI?". Unless you have a firm plan to sell your house and fully understand how much of that equity is actually available to you as opposed to being needed for your next house how do you use that equity value to calculate when you reach FI?
If you said "I'll wargame out several possible scenarios and see what they look like." I'd buy that. If you just dump all your home equity - say $500K - in with $700K investments that doesn't give you a true picture of where you stand either.
When calculating FI I don't use my home equity. I do use it to calculate my NW for shits and giggles because it's a higher number, but I am aware even in the most radical scenario for me [sell house, buy RV, hit road] I have to deduct cost of realty fees and cost to purchase a RV from my equity before I would have a useful number for FIRE planning.
I use our home equity in cfiresim calculations, because we plan on downsizing eventually. What I do is take a conservative estimate of half our house value now, and add it as "other income" in 20 years. Both the house value and year are estimates, but everything on cfiresim is an estimate. It's just a very conservative estimate.
For example, our house in Toronto is worth about (cough) $2MM right now. How can we not include it at all? In cfiresim I "only" value it at $1.5MM because I don't believe the past year's crazy run-up will stick. I increase the value by inflation only, over the next 20 years (very conservative). I assume we will be able to downsize to a place less than $750,000, thus extracting at least that amount as income.
IMO as long as I'm on the conservative side of these estimates, it's ok to use them. Nobody knows what will happen to house values in Toronto over the next 20 years, but I'm pretty sure it's safe to say we can somehow extract $750k. Even if the market for detached houses falls 60% over the next 20 years, we will still be ok, because we can sell and rent somewhere cheaper. If the market falls that hard, there will be super cheap places to rent elsewhere.