OK.
Teen births are about 2% of all live births (though you don't mean people age 18 and 19 do you, you mean the 15 year olds who need loads more help, but let's stick with this). There are about 650,000 births per year in the UK. Obviously there are more teen mums walking around than there are births per year because everyone who was a teen mum last year is a "teen mum" for life. So taking people whose children are still under 18, there may be 234,000 teen mums around with youngish children, taking care of their children, at any given time.
There are about 18 million women in the UK between 15 and 50 at any given time. Take off the 234,000 of that cohort who are themselves teen mums and that's about 17.7 million women in the UK.
How many women out of those 17.7 do we think really do disapprove of teen mums and think they are selfishly costing the state? Well, Charities say that teen mums are often abused, and I take lived expertise as really strong evidence when the themes are identified and brought together by civil society voices. So I believe there is stigma. Let's say, again to be super generous to OP and to the lived experience of stigma, that 1/3 of all women, of this childbearing age group also disapprove of teen mums.
That's an assumed 5.9 million women age 15-50, who have not themselves been teen mums, and who could think teen mums are selfish spongers, and say so.
Per year there are 15-17,000 NHS funded IVF treatments. Let's generously say the figure for individual women having an ivf cycle each year is 15,000 because some will have 2 or 3 cycles allowed so some of them are the same women.
We can't see how those groups overlap- "choosing to have ivf" and "hating teen mums".
But... - EVEN IF ...
Out of all the 15,000 women who have ivf for free, on the NHS, every single one of those women happens to also be in the group of 5.9 million who hate teen mums...
That's only 2.5% of the women, max, who already hate teen mums, choosing to have IVF.
That seems a very high figure - all the IVFers wouldn't hate teen mums, surely. Let's say the opinions of women having IVF are the same as the opinion we have assuumed for the general population. Maybe 5,000 of them (one third) disapprove of teen mums.
So the hypocritical group you are slagging off amounts to 5,000 women per year, or 0.03% of women you might meet in the UK who are of childbearing age. And that's the absolute max I reckon.
I don't think anyone should hate teen mums by the way, and I'm not sure those who do are basing it on the cost to taxpayer.
However if you know 20 of those 5,000 women personally (unlikely!) I'm sure it seems very annoying. Or even if you know one, which seems more likely from your OP.
But there are hardly any of these people with these attitudes in the grand scheme of things. Ignore them.
Be compassionate to both teen mums and infertile people.