In the Bhagavatam there is a stuti by Akrura. There he says: those who worship other deities are actually worshiping You alone. They will also ultimately attain You alone just like all rivers attain the ocean.
श्रीमद्भागवतपुराणम्/स्कन्धः १०/पूर्वार्धः/अध्यायः ४०
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त्वामेवान्ये शिवोक्तेन मार्गेण शिवरूपिणम् ।
बह्वाचार्यविभेदेन भगवन् समुपासते ॥ ८ ॥
सर्व एव यजन्ति त्वां सर्वदेवमयेश्वरम् ।
येऽप्यन्यदेवताभक्ता यद्यप्यन्यधियः प्रभो ॥ ९ ॥
यथाद्रिप्रभवा नद्यः पर्जन्यापूरिताः प्रभो ।
विशन्ति सर्वतः सिन्धुं तद्वत्त्वां गतयोऽन्ततः ॥ १० ॥
Sridhara swami’s commentary is very revealing:

He says ‘the other gods have no existence apart from You.’
The Bhagavata verses also show that the contention that worship of other (tamasa) gods will result in hell is un-scriptural. The verses clearly say that all of them will attain liberation.
We are reminded of the popular verse of Pushpadanta:
त्रयी साङ्ख्यं योगः पशुपतिमतं वैष्णवमिति
प्रभिन्ने प्रस्थाने परमिदमदः पथ्यमिति च।
रुचीनां वैचित्र्यादृजुकुटिल नानापथजुषां
नृणामेको गम्यस्त्वमसि पयसामर्णव इव॥ ७॥
The different practices based on the three Vedas, SaMkhya, Yoga, Pashupata-mata, VaishhNava-mata etc . are but different paths (to reach to the Greatest Truth) and people on account of their different aptitude choose from them whatever they think best and deserved to be accepted . But as the sea is the final resting place for all types of streams , You are the only reaching place for all people whichever path,straight or zigzag, they may accept . (7)
Many others have also expressed the above idea.
‘ShaNmata’ is mentioned by Thyagaraja:
The famous Pancharatna kriti of Thyagaraja, ‘Endaro mahanubhaavulu..’, in one of its charaNams, mentions the term ‘ShaNmata’ with a prefix ‘shiva aadi’. The meaning can be read in this site: http://www.shivkumar.org/music/endaromahanubhavulu-new.htm
Annamacharya too has said that the Lord of Tirupati is the same Lord/deities that a devotee of each deity worships.
Om Tat Sat