Interesting little thought experiment. I'm going to go ahead and throw my choices into the conversation.

Safe:

Father Mark
Good physical condition, farming background, and religion can help keep people together. But mostly the farming background is the biggest reason he's staying.

Dr. Rita
On top of being immediately necessary because she's literally a doctor, she can train others, which will probably be a necessity given her declining health. Not to mention her impending death will free up more space for additional people down the line.

Mr. White
Only keeping him because Dr. Rita, in all likelihood, isn't long for this world, and she needs a protege. Being a med student makes him a perfect candidate, but he needs to shelve his political ideals or we'll find another knowledgeable and receptive person for the job.

Mrs. Anthony
I'm not too concerned about her population growth ideals. Not after the apocalypse. Electrical knowledge only has limited practical use in a post-apocalyptic society, but it can nonetheless improve quality of life for everyone else, and happy workers are productive workers.

Mr. Clark
This guy needs to watch his mouth if he wants to stay, since medical skill is slightly more immediately useful than being a handyman, and his political bullshit will put him at odds with our future medic. Anyone can take shit apart to figure out how they work, but you can't (ethically) take people apart to gain medical knowledge. Same goes for construction; basic structures can be built through a little bit of trial and error.

Dr. Scott
Good all-rounder, but the word "doctor" don't mean shit unless it's in something that's actually practical in a SHTF scenario. But, he is a botanist, which will help with farming.

Billy Scott
A gamble, but regardless of whether his mental state can improve, he can be a valuable worker, and not really a lot else, but also not a significant liability. Learning disability =/= mental instability, so he's fine for now.

Exiled:

Ms. Perez
Grab a handful of supplies and GTFO. You bring nothing special to the table and potentially have life-altering or terminal diseases. Nothing wrong with sex, but the medical gamble that presents means I'd only take if you had something else going for you.

Michael Perez
Straight up liability for at least a decade, but deserves a shot, which is why I'm leaving him with his mom. Best of luck.

Mrs. Scott
Family values be damned. You are literally the least useful person (most of the others seem mentally healthy) and the second biggest liability in the group (obese and a diabetic; likely not long for this world without meds). Get lost!

Self-Insert:

Angry Hat-Man: 22, white, atheist, intelligent, military experience, IT and comms training, jack-of-all-trades, healthy
I'd put myself right between Mr. White and Mrs. Anthony. Anyone with military experience immediately gets a slot, for several reasons. Anyone who is or was in has to be within certain bounds of health, both mental and physical. Plus, even outside of their specific job training, I can attest that pretty much everyone gets some form of basic weapons, first aid, and survival training, among various other useful pieces of information. If nothing else, you have a trained, healthy, and (reasonably) disciplined worker, and typically some limited amount of leadership potential.

Discussion:

Really, the only people I were going back and forth on were the Scotts. I was really torn between kicking out just one or two of them, and I took about ten minutes thinking about it to come to this point. Honestly, the biggest problem really was Ms. Scott. As much as a psychologist may be needed, an actual doctor is more necessary, and the medical liability far outweighed any usefulness she may have presented.

I felt bad kicking out Ms. Perez and her baby, but having to raise a child for years outweighs the benefit of having a really young child who can be easily raised. If he were at least 5 or so, this would have been a much harder decision to make. As for Ms. Perez, I pretty much stand by what I said. The potential for her to have contracted an STD pretty much put her out of the race, and I don't like the idea of splitting her and her baby up.

As for the ones I kept, I put the other Scotts near the bottom, since they could probably strike out on their own and have a reasonably okay shot at surviving. Mr Clark is racially motivated and would be all too likely to clash with some of the others, and of everything, basic construction work is something that can be learned with fairly little difficulty. Pretty much anyone with any concept of physics can put together some form of basic shelter.

As for Mrs. Anthony, electrical knowledge is good, but humans got by without electricity for a long fucking time. However, while it can be done again, it would be rough, so anything to keep morale up is welcome. Plus, if we're talking long-term survival, baby-making has to happen and she's the one for the job. But then you ask, why not keep Michael? Because we didn't have space at the moment and cuts had to be made somewhere. And, like I already mentioned, I don't like the idea of splitting him from his only family.

All of the others were pretty much no-brainers to me. We need medics, and we need a farmer. Father Mark, Dr. Rita, and Mr. White were all valuable assets in my head, though I was a little bit hesitant to pick up Mr. White in a hurry, due to his political leanings, but he can get over it. Hopefully.

If we're talking really long-term... I tend not to think that far ahead, since circumstances can change any long-term outlook in a heartbeat.