It is not contradicting. The context is continued in the next verses. Also some verses are not translated properly in the translation you have provided.
The Linga Purana quote is
वैश्यानां नैव शूद्राणां शुश्रूषां पूजकस्य च |
स्त्रीणां नैवाधिकारोऽस्ति पूजदिषु न संशयः || 2.20.2
Neither the Vaishyas, nor the Shudras are not eligible for the obedient worship of Shiva. Also the women don't have the eligibility. There is no doubt about it.
स्त्रीशूद्राणां द्विजेन्द्रैश्च तत्फलं भवेत् |
नृपाणामुपकारार्थं ब्राह्मणद्यैर्विशेषतः || 2.20.3
Women, shudras can avail the worship of Shiva(through priests). The worship done through a priest yields results. For the well being of the rulers and others, Brahmanas should worship Shiva.
एवं संपूजयतेयुवैं ब्राह्मणद्याः सदाशिवं |
इत्युक्त्वा भगवान् रुद्रन्नस्तन्नैवान्तरधात्स्वयं
In this way, the worship of Shiva should be done through Brahmanas. Having said thus, Lord Rudra disappeared by himself from the scene.
The verses were speaking on how the worship should be done through the priests. The verses are speaking about ritual worship. They say Brahmanas are eligible to worship Shiva ritualistically.
In the verse 2.30.1, Vaishyas, shudras and women are included. In the verse 2.20.2, Not only sudras, women are also added. This was not provided in your english translation.
So Linga Purana verses are not stopping women to worship Shiva. It is prescribed through a priest. Brahmanas and kings should worship for the welfare of the others. This was the meaning here.
So, the Shiva Purana verses do not contradict with Linga Purana verses.
The translation of the Shiva Purana verse Visyeshwara Smahita 17.34:
The more an aspirant repeats this mantra, greater is the Shiva's presence in his body. For the woman devotee of Shiva, the symbol of Goddess shall be the form of concentration. (Motilal Banarsi Dass Translation)
So, it is clear that women are not barred from the worship of Lord Shiva. Linga Purana is speaking about ritualistic worship and worship through priests. It did not stop people to have devotion towards Shiva.
I have provided own english translations for Linga purana quotes 2.20.2,3. If someone has more accurate ones, please notify me. I will improve them.