I don't count my home equity in my NW, but I also don't subtract my mortgage.
My house's valuation has gone down from what I paid (in 2006), but I'm not underwater--when/if I sell, I'll at least make something. For purposes of making future plans, I think it's more accurate to use my liquid investments and count my mortgage as a monthly expense than it would be to factor my home & mortgage into NW.
And you would be wrong to do so.
Net worth means a very specific thing. It is what you own minus what you owe. Period. Your house belongs in any valid net worth measurement.
As for making future FIRE plans, that's a very different thing. Net worth means nothing in that regard. Your sustainable passive income is what matters. So, you should be measuring your sustainable passive income, which can come in many different forms.
Don't screw around with the meaning of Net Worth because you want a different measurement. Just use the measurement you need instead.
I measure passive income from social security, disability, farm income, rental house income, and a stock/bond portfolio. Net worth is useless for all of them, including your modified definition of net worth.