Knoert, those things at Linfield still happen though very rarely they will get explicit and it has improved a lot so many games no sectarian outings happen at all. If they do happen, which is a minority of games, it is often in a more subtle form rather than singing violent songs about Irish catholics. I have attended several Linfield games myself when I lived in NI, and never heard any really insulting song towards Irish catholics. I did see one time that an idiot burnt an Irish flag but he was very heavily criticised by hundreds of other Linfield fans who used the fans website to apologise for the behaviour of this one guy (who, so I have heard, rarely attends games)
They do sing God Save the Queen sometimes, waive Union Jacks etc... But they do that against "other protestant teams" as well, and even when playing against a more catholic-orientated team you can consider waiving a national flag hardly sectarian. If you do consider it sectarian, Cliftonville are just as guilty as Linfield.
As for Queens: their team is in third division, made up entirely out of staff of the university and students. They have no specific religious and political background as students and academical staff are from both communities. The team has no own ground they use for games, they instead groundshare with PSNI FC (that is the policemens team) who have a very tiny stadium with a stand holding approx 50 people. The grass pitch however is so good there that the Northern ireland team often uses it as training ground. This little stadium is in the outskirts of South Belfast and both Queens University and the police team PSNI FC play their league games there. Because the ground is owned by the police, you need to show your passport or ID when entering the ground. Queens Unis team attracts 10 to 20 fans only and most will be either family of the players or befriended other students.
PSNI itself is the same story: also in 3rd division just like Queens University FC, and also attracting not more than 10 to 20 fans who will be either relatives of the players or other policemen watching their colleagues play. I did attend one PSNI away game and there were 5 of their fans, including one in police uniform
But while Queens Uni is a politically neutral team, PSNI is the same in theory but often seen as a protestant team because in the past the police employed more protestants than catholics (is not the case anymore as far as I know)
One last thing, sorry if this borders politics: many foreigners seem to take a side for a united Ireland when it comes to the Northern Ireland issue. I must say I had this view as well in the past when I had never been to Ireland myself. However, since I have lived on the island for 3 years (of which 2 years in the north) I have sort of adopted a more neutral viewpoint. because the issue is a lot more complex than saying "it is one island so it should be one nation". The British did build very good infrastructure on the island and helped a lot to develop the island (those supporting a united Ireland will say they did so by forcing their own culture and traditions on the population, but that is a very onesided view) and the economy in the area only started to get off properly when the British invested in it. So while I do see several points to say a United Ireland would make sense, I also see some valid arguments why people still feel a connection with the UK. I wont go further into this because it is politics and this is not allowed here, but I am just saying that many foreigners seem to support a united Ireland while the whole issue is a lot more complex than it seems. I would invite anyone to live in Northern Ireland as well for a while like I did, and I am curious if they would change their views on the issue. I certainly have gotten a lot more insight in the complex history of the country and would no longer think in the same terms as before I lived and experienced Northern Ireland.
PS: if you visit the country, skip the second division and take a sightseeing tour. Belfast is an amazing city with not just a unique history but a great present as well. The artistic scene is big, there are some beautiful buildings all over the city, ... also, the coastal towns like Bangor and Holywood are great to visit. I would rather advise that instead of a division 2 game because honestly, D2 is terrible in terms of football and attendances... I did watch several D2 and D3 games myself but I was living in Northern Ireland and thus had all the time to see the country. If you only have a few days or a week in the country, I would advise to stick to your Linfield-Glentoran plans and use the other days to see some of the country. Northern Ireland may have a weird reputation abroad, but it is really a great place with a lot of sights worth of visiting. And definitely visit Laverys or the Limelight during the nights, on Wednesdays it is open mike night at Laverys and that is where all young artists hang out then. On Mondays there is poetry readings and traditional Irish music in the John Hewitt Pub, also worth checking!