According to the Mantrayogasamhita, different people with different mental inclinations should have different deities as Ishta. Can a Vaishnava Guru give initiation by Shakti mantra or a Shaakta Guru for Vishnu/Krishna/Gopala mantra?
As noted in this answer, a Shakta should get a Shakta Guru and same for a Vaishnava.
But when a Siddha Guru is giving Mantra the disciple should not consider which Mantra it is.
Omkarnath was a Vaishnava saint. His Sampradaya was Ramanandi. But he gave Dikshas of various other deity Mantras too.
Quoting from their website:
The Ramananda sect worships only Lord Ram. Thakur's Istadev was Ram, but still, He liberalised the Diksha Parampara of His sampraday, and gave the Mantras of all Deities, as per the adhikara, background, spiritual inclination of individual devotees. Every Form of Lord is inseparable from Lord Ram, and Thakur's improvisation was to supplement the usual Ramanandiya customs. Even Thakur's guru [Dasarathidev], gave the Mantras of 5 deities, ie- [person in whose body SKY element is more should recieve Vishnu mantra , in the same way for FIRE element Shakti Mantra , for EARTH element Shiva Mantra , for AIR element Surya mantra & for WATER element Ganesh Mantra .]
So, there seems to be no problem if the Guru is Adhikari (competent) and I think this competency comes from Krama Dikshas, Purna Abhisekhas.