Well, she did hold a very high office in government. Even if she is unpopular to some I'm sure there are just as many that view her in a positive light. I don't know much about her or the reasons behind the like and dislike but what I do know is that she spent a lot of time working to do the best she could for her country. While you can argue how "fancy" (for lack of a better word) the funeral should be it seems only fair that after all she gave and did for the country she should receive a state funeral.
So just because the Royal Family has a lot of money they should pay for it? Why not just make everyone who makes X pounds per year pay X pounds to pay for the funeral?
I can argue that the Royal Family do a ton more than the PM since PM's come and go and being Royal is a life time job that only ends on death.
Their lives are in service of the country, those in parliament and the PM's need to try and beat the other party every 4-5 year's and then they are gone.
Sure she was around for 11 year's but that was 11 years of what people see as hell, except for the Falkland war.
Also doing that would be making companies pay for the funeral and we all know the government hates to tax companies, well the massive ones anyway.