Can We Take Prasada Offered To Shiva?

Yes, absolutely.

There is a propaganda and misconception that naivedyam offered to Lord Shiva should not be consumed.

References from Scriptures given below make the greatness of Shiva prasada (naivedya) amply clear.

There are six types of Shiva-nirmalyam -

देवस्वं देवताद्रव्यं नैवेद्यं च निवेदितम् ।

चण्डद्रव्यं बहिःक्षिप्तं निर्माल्यं षड्विधं स्मृतम्म् ॥

1. Devaswam - Land, building, people, etc. belonging to Shiva. 

You should not use them for your personal purpose. 

Also servants of Shiva should not be used for your personal purpose even if you are paying their salary.

2. Devatadravyam - Gold, silver, gems, etc. belonging to Shiva.

They should never be used for any other purpose.

3. Naivedyam - Food, drinks, flowers, garlands, etc. prepared for Shiva but not yet offered to Shiva.

They should never be consumed or used for any other purpose.

Out of the six, the above three should never be used.

एतस्त्रिविधनिर्माल्यमनर्हमिति कथ्यते ।

शिवद्रव्यापहारेण नरकं यात्यसौ जनः ॥

Those who partakes of or misuse the above will suffer in Naraka.

4.Chandadravyam - Chandeshwara has the first right over offerings made to Shiva. In temples following the established tradition as per the Agamas, offerings such as food and garlands are offered to Chandeshwara after they are offered to Shiva.

You should not take the offerings before they are offered to Chandeshwara.

It should not be noticed that this right of Chandeshwara does not exist in Shiva Lingas that are Swayambhu, Banalinga, linga made from metals, Siddha Lingas and idols.

5. Bahi-kshiptam - Garlands, etc. thrown out from the Garbha griha.

They can be taken as prasada.

6. Niveditam - Food, drinks, flowers, garlands, etc. already offered to Shiva.

These are distributed as Shiva-prasada.

It is a blessing to receive and partake of them.

Benefits of consuming Shiva Prasada

यो वा शिवस्य नैवेद्यं भुञ्जीत समतीत्येव दुःखं सर्वमैश्वर्यमाप्नोति । (निर्माल्यरत्नाकरम्)

One who consumes food, etc. offered to Shiva will overcome all miseries and attain prosperity.

रुद्रेणात्तमश्नन्ति रुद्रेण पीतं पिबन्ति रुद्राघ्रातं जिघ्रन्ति तस्माद्ब्राह्मणाः प्रशान्तमनसो निर्माल्यमेव भक्षयन्ति । (जाबालोपनिषत्)

The noble-minded eat only whatever is eaten by Shiva, only drink whatever is drunk by Shiva, and smell whatever is smelled by Shiva.

दृष्ट्वापि शिवनैवेद्यं यान्ति पापानि दूरतः ।

भुक्तेऽपि शिवनैवेद्ये पुण्यान्यायान्ति कोटिशः॥ (ब्रह्माण्डपुराणम्)

Even if you see Shiva-naivedya from a distance, all your sins run away. If you consume Shiva-naivedya, you will acquire punya in crores.

अलं यागसहस्रेणाप्यलं यागार्बुदैरपि ।

भक्षिते शिवनैवेद्ये शिवसायुज्यमाप्नुयात् ॥

Eating Shiva-naivedya is greater than performing millions of yajnas because it will give you Shiva-sayujya.

यद्गृहे शिवनैवेद्यप्रचारोऽपि प्रजायते ।

तद्गृहं पावनं सर्वमन्यपावनकारणम् ॥

If Shiva-naivedya enters a house, it becomes pure. That house purifies the entire neighborhood.

आगतां शिवनैवेद्यं गृहीत्वा शिरसा मुदा ।

भक्षणीयं प्रयत्नेन शिवस्मरणपूर्वकम् ।

You should receive Shiva-naivedya with respect and consume it thinking about Shiva.

आगतं शिवनैवेद्यमन्यदग्राह्यमित्यपि ।

विलम्बे पापसम्बन्धो भवत्येव हि मानवे ।

It is sinful not to consume Shiva-naivedya that comes to you.

सर्वेषामपि लिङ्गानां नैवेद्यं भक्षयेच्छुभम् ।

Naivedya offered to all kinds of Lingas are auspicious.

ब्रह्महाऽपि शुचिर्भूत्वा निर्माल्यं यस्तु धारयेत् ।

भक्षयित्वा द्रुतं तस्य सर्वपापं प्रणश्यति ।

Even if someone has committed Brahmahatya, he is relieved of his sin if he eats Shiva-naivedya.

मदीयभुक्तं निर्माल्यं पादाम्बु कुसुमं जलम् ।

धर्ममर्थञ्च कामं च मोक्षञ्च च ददते क्रमात् ॥

Remnants of Shiva's food gives spiritual elevation, his charanodaka gives wealth, flowers offered to him gives attainment of desires, and water offered to him (abhisheka) gives moksha.

In conclusion, it is a blessing to get the opportunity to receive and take food offered to Shiva.