Question
How are gods and goddesses such as Shiva and Shakti seen in the Vaishnava sampradayas?
Answer
You have asked :1. Are the various devatas manifestations of aspects of the Supreme God or are they subservient to the Supreme God, as is the view in orthodox Gaudiya Vaishnavism?
2..How is Shakti/the consort of Shiva (including her various forms such as Kali, Durga, Parvati, Tara, etc.) seen in the various Vaishnava sampradayas?
Let me answer your question from the Gaudiya-Vaishnava perspective, as you failed to understand the use of the word 'demi-gods' by some followers of the Gaudiya Vaishnavas.
The Gaudiya Vaishnava sect originate from Mahaprabhu Sri Krishnachaitanya Who is regarded by many (including myself) as an incarnation of God. So we must focus on His and His direct disciples' views on this topic. In the Sri Sri Chaitanya-Charitamrita, we find Sri Chaitanya saying :
isvaratve bhed maanile hay aparadh/ ek i iswar bhakter dhyan-anurup(2/9/139-42)
which means : Its a sin to differentiate between various forms of God. God is one Who takes many forms as per the inclination of the devotees.
The above quotation shows how broad-minded Mahaprabhu was, as is expected from an incarnation like Him. So He would never accept a word like 'Demi-God'. Let us now come to Shiva and Shakti.
Gaudiya Vaishnavism on Shiva:
In Navadvip, Mahaprabhu has assumed different forms of God. In Murari Gupta's karcha(2/11), SriChaitanya-Bhagavata(Madhya, chapter 8) and Sri Chaitanya-Charitamrita (1/17), we have the description of Mahaprabhu taking the form of Shiva. 'He says :'I am Shiva' His devotee Mukunda Dutta chanted the Shiva-Mahimna-Stotra (Murari Gupter Karcha, 2/11/17).Mukunda Dutta was an ardent devotee of Mahaprabhu. The Shiva-Mahimna-Stotra that he chanted is a famous hymn composed by Pushpadanta.In this hymn, Lord Shiva is described as the Supreme Godhead:
traiyi saamkhyam yogah pasupatimatam vaishnavam iti prabhinne prasthaane paramidam adah pathyamiti cha ruchinaam vaichitryaad riju-kutila-naanaapthajushaam nrinaam eko gantavyas twamasi payasaam arnava iva (7)
meaning : Oh Shiva, as all rivers merge at the end with the sea, you are the goal of all human beings. They accept different straight and complicated paths like that of the Vedas, the saankhyas, the yogis, the paasupatas, the vaaishnavas merely because of difference in their mental inclinations.
This makes the concept of the Gaudiya Vaishnavas on Shiva vary very clear.We read in Sri Chaitanya-Bhagavata (Antya khanda):
siver gaurab bujhaaen gaurchandra/ eteke sankar-priya sarva-bhakta-vrinda// naa maane chaitanya-path bolay vaishnav/shivere amanya kare byartha taar sab//..pujaye govinda jena naa maane shankar/ ei paape aneke jaibe yamaghar
meaning: Sri Gaurchandra(Sri Chaitanyadev) makes all understand Lord Shiva's glory. So all His devotees worship Shiva. Someone not obeying Sri Chaitaya and calling self a vaishnava will be cursed by Lord Shiva and be ruined. Many worshipping Sri Krishna do not worship Lord Shiva. These people are sinful and will go to hell.
Gaudiya Vaishnavism and Shakti (Kali,Durga, Parvati)
Sri Chaitanyadev was born in Navadvip which is in Bengal. Bengalis are very devoted to Devi Shakti. Sri Sri Devi-Mahatmya, a part of Markandeya-Purana is highly respected by the bengalis.Mahaprabhu Himself copied this book and gifted to one of His relatives. In Sri Sri Chandi, we get
Devya yayaa tatam idam jagad aatma-shaktyaa nihshesha-devagana-shakti-samuha-murtyaa/ taam amvikaam akhila-deva-maharshi-pujyaam bhaktyaa nataah sma vidadhatu shuvani saa nah (mantra 3, chapter 5)
meaning : We bow down with devotion to the Mother Goddes, Who has covered the entire world with Her own power and Who is worshipped by all devas and rishis.May Devi provide us with all good.
yasyaah prabhabam atulam bhagavaan ananto brahma harascha na hi vaktum alam valam cha sa Chandika akhila-jagat-paripaalanaya nahaaya cha asurabhayasya matim karotu (mantra 4)
meaning: Even Lord Vishnu, Brahma and Shiva are unable to describe Her unparallel effect and energy. May that Devi Chandika wish for preserving the world and destroying the fear from demons in us.
Someone accepting Sri Sri Chandi is therefore bound to accept the Mother Goddess as the Supreme Godhead.
Sri Chaitanya-Bhagavata (along with other biographies mentioned above) describes how Sri Chaitanya Himself assumed the form of Devi Chandi and the devotees started uttering hymn
jaya jaya jagata-janani mahamaya/ dukkhita jibere deho charaner chhaya// brahma-vishnu-mahesware tomar mahima/ balite na paare anye ke dibek sima//..tumi adya avikara parama-prakriti/jagat-janani tumi dvitiya-rahita//
meaning : Glory to thee O Mahamaya,the Mother of the world! Please give the suffering people resort to your feet. Even Brahma, Vishnu and Shiva can not describe your glory, then what will the others tell about you? You are the Primal Origin devoid of any change. O Mother of the world, You are One without a second.
If She is One without a second, can Sri Krishna be different from Her? Absolutely never.Sripada Jiva Goswami therefore quotes a sloka from Gautamiya-Kalpa:
yaa durga saiva krishnah syaad yah krishnah durga eva sa/anayor antaradarshi sansaraad na vimuchyate//
meaning: Durga is one with Krishna and Krishna is one with Durga.Whoever sees them as two can never be liberated from worldliness.
Mahaprabhu Himself used to go to temples of Shiva, Rama, Nrisimha, Durga,Bhairavi and worshipped all. Yes, He preached the worship of Lord Krishna, but has instructed His devotees:
Anya deva anya sastra ninda naa karibe. meaning never criticise other forms of God. By the way, Sri Nityananda Mahaprbhu, who is also worshipped by the followers of Sri Chaitanyadeva worshipped Lord Shiva and Devi Shakti regularly.
Hope the above throws some light on the topic you questioned about.
Referencees: 1.Chandi-Chinta by Dr.Mahanambrata Brahmachari,Mahanaam Angan, 2.Gaudiya Vaishnava Darshan by Radhagovinda Nath, Sadhana Prakashani, 3.Mahaprabhu Sri Gauranga by Radhagovinda Nath,mSadhana Praakashani,4.Sri Sri Chaitanyadeva by Swami Saradeshananda,Udbodhan.
Update
Srila Sripada Radharaman Charan Das Babaji was a renowned Gaudiya Vaishnava saint contemporary of Sri Ramakrishna.Its He who established temples at all the places Mahaprabhu visited. According to Him:
Who attract the soul of the devotees is Hari.The Shaivas should relate this word to Surya, the Shaktas to the Mother Goddess, the Shaivas to Lord Shiva and the Vaishnavas to Lord Vishnu. No pesonal or secterian system or behaviour can be universal.(His biography by Ava Sarkar,Pustak Vipani, page 16).There is no difference between Kali,Durga,Shiva, Vishnu, Nitai,Gaur etc because God is Purna Purnatama(Ibid page 17).
This also is in perfect confirmity with what has been mentioned in the answer.
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