It is not permitted for Muslim's to celebrate Saint Valentine's Day (see question 37908). However, there is no scholarly opinion that celebrating Saint Valentine's Day is shirk or kufr at large. Doing so may lead one, though, down that path to shirk or kufr.
Ibn Taymiyyah said:
فلا فرق بين مشاركتهم في العيد وبين مشاركتهم في سائر المناهج، فإن الموافقة في جميع العيد، موافقة في الكفر. والموافقة في بعض فروعه: موافقة في بعض شعب الكفر، بل الأعياد هي من أخص ما تتميز به الشرائع، ومن أظهر ما لها من الشعائر، فالموافقة فيها موافقة في أخص شرائع الكفر، وأظهر شعائره ولا ريب أن الموافقة في هذا قد تنتهي إلى الكفر في الجملة بشروطه
— NOTE: My own translation, so treat with care:
For there is no difference between their participation in the festival and their participation in the other methods. An endorsement of their festival in its entirety is an endorsement of the disbelief. A partial endorsement of some of its [the festival] aspects is a partial endorsement of disbelief. Festivals are most characteristical of the laws [of religion] and one of the most apparent of its rituals. An endorsement of the most characteristical of the laws of disbelief and display of its associated rituals may, without doubt, lead one to disbelief in its entirety while fulfilling all of its conditions.
— Iqtidā' as-Sirat al-Mustāqīm, Vol. 1, pp. 528-530
As you can see, Ibn Taymiyyah just fell short of labeling one who celebrates the festivals of non-Muslims as a kafir or mushrik. Nonetheless, he expressed quite strongly that doing so may lead one down the path of fulfilling all conditions of kufr.
Ibn Qayyim al-Jawziyya did not have a different opinion as he said:
وأما التهنئة بشعائر الكفر المختصة به فحرام بالاتفاق مثل أن يهنئهم بأعيادهم وصومهم، فيقول: عيد مبارك عليك، أو تهنأ بهذا العيد، ونحوه، فهذا إن سلم قائله من الكفر فهو من المحرمات، وهو بمنزلة أن يهنئه بسجوده للصليب، بل ذلك أعظم إثما عند الله وأشد مقتا من التهنئة بشرب الخمر وقتل النفس وارتكاب الفرج الحرام ونحوه
— NOTE: My own translation, so treat with care:
As for congratulating non-believers on the methods of disbelief specific to their belief, this is not permitted by agreement [of scholars], for instance, by congratulating them on their festivals or upon their fasting by saying "blessings of the festival for you," or "enjoy your festival," and so on. This, if the person saying is saved from becoming a disbeliever, is strictly forbidden, and it is the same as congratulating one for prostrating to the cross or even more of a sin for Allah and more hated than congratulating one on drinking wine or killing a soul or fornication or otherwise.
— Ahkām Ahl adh-Dhimma, Vol. 1, pp. 441
Ibn al-Qayyim obviously shares the same opinion as Ibn Taymiyyah. Both scholars on different occasions attributed their strong statements to the hadith narrated through Ibn 'Umar that said that those who copy a certain group of people become one of them, so copying disbelievers' rituals may make one become a disbeliever oneself:
حَدَّثَنَا عُثْمَانُ بْنُ أَبِي شَيْبَةَ، حَدَّثَنَا أَبُو النَّضْرِ، حَدَّثَنَا عَبْدُ الرَّحْمَنِ بْنُ ثَابِتٍ، حَدَّثَنَا حَسَّانُ بْنُ عَطِيَّةَ، عَنْ أَبِي مُنِيبٍ الْجُرَشِيِّ، عَنِ ابْنِ عُمَرَ، قَالَ قَالَ رَسُولُ اللَّهِ صلى الله عليه وسلم: مَنْ تَشَبَّهَ بِقَوْمٍ فَهُوَ مِنْهُم
Narrated Abdullah ibn Umar: The Prophet (ﷺ) said: He who copies any people is one of them.
— Sunan Abi Dawud, Book 34, Hadith 12