I basically always grab Humanism first. Secularism is at its weakest early on when you're just working Unis and Guilds. It will give you 22-24 bpt at that point (if you're working all 3 guilds, which you usually aren't, but let's assume best case scenario anyways) but that's not better than rushing out Free Thought the vast majority of the time. Moreover, you have to remember than Humanism math is very difficult to determine. It either gets you extra GSes that you wouldn't have gotten otherwise or it doesn't. Even if you can work that out to be an average value in theory, in practice there's no such thing as a an average value when it comes to generating a GS. It either gets produced or it doesn't. I like getting Humanism early on because it maximizes the odds that you will, in fact, get that extra GS for that extra late-game bulb. You never know exactly on what turn you'll get your Schools + Labs so it's pretty hard to determine exactly how many GSes you'll generate that early on. Secularism doesn't have a "useful life" timer like Humanism does so I feel fairly safe taking it third.
Free thought will almost always generate more science than Secularism does unless your population is low and figures to stay low well into turn 160 or so. Since that's usually not the case you're usually missing out by not grabbing it as soon as possible.
Here's a SS from a Shoshone game that I played earlier today. It's turn 157 and I'm producing 350 bpt. I did not rush Secularism this game. I rushed Free Thought. My cities are growing like they should be and so I'm getting most of my science from population and % modifiers. The 24 from Secularism isn't doing that much for me any more. It's also worth noting that I got a GS roughly 12 turns before I won the game and used it to bulb Particle Physics. Had I waited I probably wouldn't have gotten those free 8 turns shaved off of my clock. Anecdotal evidence, sure, but getting it first probably made the difference.
Sadly, maths will prove you wrong 99.9% of the time on this. I am actually surprised to see a very successful deity player not pick secularism immediately. It is extremely potent.
Let's take a reasonable simple game setup and accept some math simplification hypotheses.
3 city setup. No observatories for simplification (observatories favor secularism over free thought) and no city growth between first policy and third policy (this slightly favors free thought over secularism).
We just hit T120 and can pick one of the 3 policies, we will get the 2nd SP on T 135 and the third on T150. We work 0 TPs, growth still matters too much.
Cap size 18 (nc built)
city 2 size 14
city 3 size 12
Cap works both uni slots and 2 GW slots
city 2 works both uni slots and 2 GA slots
city 3 works both uni, no GW yet.
Before any SP, BPT on T120 is calculated as follow:
(18+9+3+6)*1.83 + (14+7+6)*1.33 + (12+6+6)*1.33 = 133.71 BPT
Scenario1 - Secularism
Your science immediately jumps to
(18+9+3+14)*1.83 + (14+7+14)*1.33 + (12+6+10)*1.33 = 164.31 BPT
Net gain of 30.6 BPT for 30 turns, grand total of 918 beakers from the secularism path
Scenario2 - Humanism
You gain 15 turns worth of +25% GPP for GS. This effectively means 1.5 GPP per turn per city for a total of 1.5*3*15=67.5 GPP
You gain Free thought on T145 at which point, your science jumps to
(18+9+3+6)*2.0 + (14+7+6)*1.5 + (12+6+6)*1.5 = 148.5 BPT
Net gain of 14.79BPT for 15 turns or 221.85 beakers
So basically, the tradeoff between the 2 paths in the setup mentioned above is of roughly 700 beakers for 67.5 great scientist points.
I don't know how much you value GPP but unless those 22.5 points in a given city would've allowed you to grab an additional GS in the late game for a bulb, it nets out to however many extra beakers you get from working the academy tile 2-3 turns earlier which is worth approx. 32-48 beakers total.
To have a better picture, you would need to run a spreadsheet, add the growth of each city and add any existing academy in the equation. Realistically though, 17% science from even 2 academy (which is quite generous to have on T135, you basically need to be Babylon or hit pisa), the free though bonus to each academy is worth 20.4 beakers over the 15 turns. We're still faaaar off the 700 beakers to bring them to par.
When could free though be better? You work nearly 0 specialist slot because for whatever reason you need to grow. Or you are working a hefty amount of TPs (you'd need to work about 25 TPs in non puppets or 25/.75=33.3 tiles from puppets.
If you have any observatory in cities where you work specialists, the favor shifts even further towards secularism.
If you have more cities working even just 2 scientist slots, it shifts again more towards secularism especially at lower pop cities (eg 4 cities size 15/10/8/8 working only all scientist slots)
This doesn't include the longer term mini snowball effect from reacing scientific theory approx. 3 turns earlier! etc.