Can people worship Vishnu and Shiva together in the same temple?

 Surely of course why not, Yet Ishta must be one only, So decide first who is your Ishta. The best way to chose is from heart, or contemplate yourself, what you want, and how you see world, Now if you want Gyan, Ananda ,material and spiritual benefits than Shiva shall be Ishta. If you can not fathom great god, and feel comfortable in certain God having human attributes who comes and lives like them between them and you want some master over you and see yourself as Dasa than Vishnu shall be your Ishta.

In short those who have got elated who want ever present subtle bliss, powers and ultimate self realization than Shiva is only way, Those who are mundane can not fathom greater vedic concepts of truth of adwait nonduality, and want to see God under human mind based emotions, and have strong identification with mind body and search god outside as some human like them having emotions than Vishnu is right way.

Shastra says, for both like I am Staunch Shaiwaite, but when i worship shiva then i would worship Ganesh Durga Kartik Surya and Vishnu also, chant his name and stuti offer him chandan pancopchar etc actually to Panch Bramhan, and we dont degrade Vishnu like jealous insecure cults of madhavcahrya nd isckonites do to all sanatana gods.

And if you are Vaishnava than also you must worship Panch bramhan too and Shiva specially , because Shiva is Ishta of Vishnu, there is no Ishta of Shiva, what fools spread is ,mere false hearsay, Worshiping Shiva is must for Shaktas and Ganpatyas Saurees also, Among major Panch Bramhans, four belong to Shivas Family only.

And also, the Rule of Shastra is, If you worship all Gods, but leave Shiva than that worship is fruitless , yet if one leaves all Gods and worships Shiva Lingam only then all Gods will bless him, How this rule began, is mentioned in every single Puran.

Hence Ishta shall be one, than as per your level and heart chose god but worship both infact all Panchbramhans never degrading any one, like we dont see Vishnu surya etc different from shiva They are also forms of Shiva hence we worship them too, And same would do true Vaishnavs, like Tulsi das Chaitanya, Arjun Hanuamn and millions of true Vaishnavs worshiped Shiva. and true Shaiwas also worship Vishnu and Panch Bramhan, this truth of Sanatana Vedic Dharma.