Is severing negative communication with an "incompatible" person a big no-no in the Buddhist pracice?

I feel a sense of sadness and remorse in your question.

Now that they're gone, I wonder how a person following the Buddhist precepts would have handled this. Showing compassion every once in a while is one thing, having your life and personal space invaded with petty commands, requests and criticism day after day, even when you're trying to meditate, seems like another.

If your practice deepened by leaving, that was better for both. If your practice could have deepened by staying, that would also have been good for both. Yet if you had stayed, your practice might have gone nowhere and even descended into mutual anger, which would not have been good.

From AN4.95 we have in increasing order of goodness:

1. One who practices to benefit neither themselves nor others;
2. one who practices to benefit others, but not themselves;
3. one who practices to benefit themselves, but not others; and
4. one who practices to benefit both themselves and others.

Please note that what you did was #3 and that is better than #2. Of course #4 is best. It is also the most difficult. Do what you can and leave remorse behind. Remorse is a hindrance.

that's the opposite of your title. Severing negative communication with an “incompatible” person a big yes yes. you can tell the person that you do not appreciate what she says and you prefer to avoid her form now on.

A puthujjana will never ever become a good puthujjana by living around bad people. Even worse, puthujjanas have zero notion of morality, they do not know who are good people, who are bad people, what are good thoughts, speeches, actions, what bad thoughts, speeches, actions. Also, living alone for a puthujjana is bad idea too. Puthujjanas must live around the kalyanamittatas, meaning the admirable friends. When there are no buddha, it is hard to find such people. there are plenty of suttas about this https://www.accesstoinsight.org/ptf/dhamma/sacca/sacca4/samma-ditthi/kalyanamittata.html

living around the admirable people is the way to have sati sampajanna, or ''mindfulness'' like people say today. Once you are good at sati sampajanna, you can use sati to transform sati sampajanna into samadhi. THe buddha claims that becoming homeless is for people who are good at setting the citta into samadhi, not for people who are bad at it. Then once you are good at setting the citta into samadhi, you use sati to transform samadhi into vipassana. http://obo.genaud.net/dhamma-vinaya/pts/an/04_fours/an04.259.wood.pts.htm this is what it takes to be ready for a monk for the homeless life in a forest

Monks, if he possess four qualities a monk is fit to resort to lonely spots and solitary lodging in a forest.

What four?

Thoughts of renunciation, thoughts not malicious, harmless thoughts, or if he be not dull-witted, not an imbecile.

These are the four qualities of a monk fit to resort to lonely spots and solitary lodging in a forest.'

another sutta

"Upāḷi, it's not easy to endure isolated wilderness & forest lodgings. It's not easy to maintain seclusion, not easy to enjoy being alone. The forests, as it were, plunder the mind of a monk who has not gained concentration. Whoever would say, 'I, without having gained concentration, will spend time in isolated wilderness & forest lodgings,' of him it can be expected that he will sink to the bottom or float away.

http://obo.genaud.net/dhamma-vinaya/ati/an/10_tens/an10.099.than.dto.htm

Instead the buddha lists various dwellings what to do with them

What is good about living alone in a house, is that you can play the homeless for a few days, feeling safe by knowing that you still have a house if the situation worsens.

A Buddhist meditator eventually changes their relationships when they start to be aware of the path that leads to suffering.

Not associating with fools, Associating with the wise, Honoring those worthy of honor; This is the greatest blessing.

Either solitude or having right relationships are the main necessities for freedom from suffering.

Beings of low dispositions come together & associate with beings of low dispositions. Beings of admirable dispositions come together & associate with beings of admirable dispositions.

https://buddhasadvice.wordpress.com/friendships/

However, it is possible to create relationships with the people who have deep narcissistic personality disorder. A Buddhist meditator can come to a point that not dwelling in past so much and not clinging to self(which is just an illusion) anymore, and he/she can keep smiling and talking to a person in the evening who have just became a monster in the same day's afternoon. But this is just a gift of noble spiritual path of Buddhism. In general you have to keep your distance or cut your connection completely with people who are just harming you. Also, a Buddhist meditator have to create relationships with the people who are involved in spirituality(meditation/mindfulness) and not with the ordinary people who are completely enslaved by the evil nature of humanity. If you have to live in a difficult situation(like living in a prison for life-time etc..) then just wait to become a Sakadagami and then you will not have any problem anymore LOL. Never feel guilty for cutting your connections with narcissistic people. A narcissist can never be a "good" person, they are actually the complete opposite of the "good". Loving does not require "liking" or keeping contact with everyone.

The Pali suttas say (Snp 1.10; SN 10.12) there are four qualities for the household life (which are also to be applied to any significant relationship), namely:

1. Sacca (truthfulness; honesty; straightforwardness; openness; no secrets)

2. Dama (training in self-improvement); and Dhamma (principles)

3. Khanti (patience; forbearance; tolerance)

4. Caga (sacrifice; generosity)

Therefore, in a significant relationship, a person should truthfully communicate to the other person any concerns they have about their behaviour and both should train in self-improvement to abolish that unwholesome behaviour.

If the other person does not respond and the relationship is toxic or harmful (intolerable) then cutting ties is OK. For example, one sutta says a wife (SN 37.30) without ethics is expelled from the household.