Thank you very much for asking question presenting widespread discontent. We see two types of people around:
1. Bahu / Sarva deva upasak i.e. who worship more then one deity or all deities.
2. Eka deva upasak i.e. who worship only one God.
Corresponding to the above sentiments of devotee scripture has preached two types of
devotions:

Adhivaasan:- There are various examples of Archana Bhakti such as offering ‘Panchamrita-snaanam’ on birth ceremony of Lord, ‘Adhivasan’, ‘Sankalp’,‘Dhoopdeep’, ‘Devothhapan’, Aarti, Sankhodak etc. All these are performed as a part of a devotional worship and not independently. An Archana bhakti is one of nine rites of Krishna Worship. Adhivasan is the process in which we impose our sentiment of Krishna worship on the material things to be used as a part of Krishna worship like Hindola, Chariot, Dola etc. After ‘Adhivasan’, that material things should be treated as ‘Krishna Swaroopaatmak’ and not an ordinary thing till that particular ceremony is completed.

Anyaasray: A devotee with a desire to serve Shri Krishna, should first take diksha called ‘Nam Diksha’ which is also known as dikasha of Shri Krishna refuge (Shranagati). By this diksha a devotee is taking a refuge with Shri Krishna only. Lord Krishna in Geeta explains the same thing as follows; “Sarva dharman parityajya mamekam shranam vraj, aham twaam sarvpapebhyo mokshayishyami maa shuchah” and “Devi esha gunamayee mama maayaam durtyayaa, maamev ye prapdyante maayaametaam taranti te” menas For this wonderful illusion of Mine(Shri Krishna’s) consisting of the three Gunas (modes of nature) is extremely difficult to get overcome; those however who take refuge in Me alone (who take an absolute refuge in Shri Krishna alone) cross it”. And “Surrendering all duties to Me (Shri Krishna), seek refuge in Me (Shri Krishna) alone. I (Shri Krishna) shall absolve you of all sins, grieve not”. In other words the soul can attain liberation from this illusion, only by leaving the commitment (faith) in all means, and taking Shri Krishna’s refuge only. A true devotee of Shri Krishna should disassociate himself from other incarnations or means/acts. Shri Bhagawat also quotes “Yathaa hi skandhshaakhaanaam tarormulaavasechanam evamaaraadhanam Vishnoho sarveshaamaatmanacha hi” means by watering roots, the branches & leaves also get nourishment, similarly by offering worship to Lord Vishnu, it is nothing but worshiping all souls including self. In Geeta also Lord Krishna says “Yepyanyadevta bhkta yajante sradhhyaanvita tepi maamev kontey yajanti avidhi purvakam” means even those devotees who endowed with faith, worship other Gods, they too worship me (Shri Krishna) alone, though not in accordance with rules (without proper knowledge). Thus Anyaashray means keeping faith and worshiping any other person/thing/God other than Lord Shri
Krishna.